Questions related to Chaos
Interested in outside the box academic ideas on how exism movements can lead to the death of normal liberal democracy from within in the quest for permanent access to power?
Perhaps you should read this DRAFT paper
Rethinking democracy 107: Placing the post 2016 liberal democracy landscape under independent rule of law variability system to indicate when to expect peaceful transfer of powers and when not when parties lose elections(UNPUBLISHED).
Sharing this 2025 article on RETHINKING DEMOCRACY that just came out, you can check it when you have time
Rethinking democracy 108: Democratic and non-democratic systems: How external and internal paradigm dynamics should be expected to work under changing present-absent effective targeted chaos and independent rule of law conditions and competition for power?
(PDF) Rethinking democracy 108: Democratic and non-democratic systems: How external and internal paradigm dynamics should be expected to work under changing present-absent effective targeted chaos and independent rule of law conditions and competition for power?
Rethinking democracy 108: Democratic and non-democratic systems: How external and internal paradigm dynamics should be expected to work under changing present-absent effective targeted chaos and independent rule of law conditions and competition for power?
Have you ever read this article? They help to understand when exism movements like Brexit and Usexit should be expected to take power under majority rule liberal democracy thuinking
Muñoz, Lucio, 2018. True Democracy and Complacency: Linking Voting Outcome Expectations to Complacency Variability Using Qualitative Comparative Means, Boletin CEBEM-REDESMA, Año 11 No. 1, January, La Paz, Bolivia.
Using present-absent effective targeted chaos and independent rule of law theory where the true majority view(T) competes with the true minority view(M) for access to power, the structure of two forms of liberal democracies and permanent authoritarianism can be stated as follows,
where
E = effective targeted chaos present,
e = effective targeted chaos is absent,
I = Fully independent rule of law system is present,
i = fully captured independent legal system = Fully non-independent legal system
Normal liberal democracy = NLD = (T.M)(eI)
Extreme liberal democracy = ELD = (T.M)(EI)
Permanent authoritarianism = PA = (T.M)(Ei)
So the question: Can you see how the structure of the death of liberal democracies can be stated in terms of effective targeted chaos and fully captured independent legal systems?
What do you think?
Are you familiar with the lessons learnt from the coming and going of BREXIT/Brexism and USEXIT/Trumpism in 2016-2024?
Here is a simple academic way of looking at the NEW LIBERAL DEMOCRACY LANDSCAPE where you have normal democratic outcomes competing for power against extreme democratic outcomes….
Muñoz, 2024. Rethinking democracy 102: What are the 3 fundamental lessons learned from facing exism movements and dictatorship threats 2016-2024?. In: CEBEM-REDESMA Boletin, Año 18, Nº 11, La Paz, Bolivia.
Are you concerned about the future of democracy, locally or globally?
What do you think the fundamental lessons learned for democracy are since 2016 BREXIT?
How can we come out with a permanent shield for the continuation of democracy regardless of type of future threat?
Perhaps they coincide with my thinking.
The question is: What are the 3 fundamental lessons learned from facing exism movements and dictatorship threats 2016-2024?
What do you think?
The answer should be short as my answer is short.
Note: I am currently putting these ideas together in one article.
Exism movements since BREXIT 2016 have been described as driven by emotions leading to the idea of Emocracy/Emocracies, but as the social discontent that is usually displayed after exism movements a kind of unexpectedly come to power as traditional democratic thinking is inconsistent with their coming shows is the true majority reaction/true emotions to the realization that the unexpected by the true majority actually has happened. So there are true majority emotions and true minority emotions and targeted chaos is directed at both with different goals, one to reduce the size of the true majority voting power by any means and the other to keep the true minority engaged and overdrive by any means...,Hence, we have the idea of democracy driven by emotions and the other idea of democracy driven by targeted chaos,....And this leads to the question, Why is effective targeted chaos more than emocracy?
You are families with coming and going of exism movements like Brexism 2016-2024, Trumpism 2016-2020, Brazilianism 2019-2023, and other exism movements still active out there, and this raises the question, Can exism movements gain power and/or remain in power without the existence of effective targeted chaos?
I think No. What do you think?
Since 2016 Brexit, the world needed to change the thinking behind traditional democracy as the democratic landscape changed, yet traditional democratic thinkers and actors have been acting as if the competition for power is STILL BETWEEN NORMAL DEMOCRATIC OUTCOMES that are happy to live within an independent rule of law system, when it is no longer the case as now a new variable came into play, legal targeted chaos, that when effective it is a game changer as it leads to extreme democratic outcomes that should be expected to be unhappy living under an independent rule of law system. To be able to answer general questions as the one here, we need to rethink democracy thinking.
And this raises the question: In terms of chaos, what is the necessary and sufficient condition for authoritarianism, permanent or temporary, to come to exist and persist?
What do you think is the answer to this question is from the point of view of just CHAOS?
Perfect democracy thinking assumes no chaos so no need for independent rule of law system and liberal democracies assume the possibility of normal democratic chaos that can be sorted out by an independent rule of law system.
So when rethinking democracy we have to think now about normal chaos, targeted chaos, and effective targeted chaos affecting voting complacency under an independent rule of law system so we can explain both the coming and going of normal and extreme democratic outcomes within liberal democracies in terms of normal and extreme democratic outcome competition....,
And this raises a key current question that was made relevant by the coming and going of 2016 Brexit/Brexism and 2016 Usexit/Trumpism:
What is effective targeted chaos?
What do you think?
Keep in mind: This is an academic question, not a political one.
You have seem exism movements to come and go now(Brexit/UKEXIT, Trumpism/USEXIT, and Brazilianism/Brazilexit) from 2016, all of them have been the result of targeted chaos being effective and then being ineffective. And this raises the question then, Why is effective targeted chaos the biggest threat to existence of liberal democracies?.
What do you think?
Hint
The answer is short if you are familiar with what exism movements are and what effective targeted chaos is and that they are operating under an independent rule of law system as this is happening inside liberal democracies.
It seems to be back to square one with Brexism, Brazilianism, and Trumpism....They came and they fell in ways away from how traditional democracy theory and thinking works....I wrote since 2016 how extreme democratic outcomes can come out, how they will behave once in power and how they could persist or fall, how important effective targeted chaos is and how important the independent law system and morality is together with predictions/expectations given whether or no targeted chaos is effective or not within an independent rule of law system and majority rule.... If what happened to Brexit July 2024 is consistent with what happens in the USA in November 2024, then the outside the box theory may have several validating points. And this raises the question: Does the fall of BREXISM, Brazilianism and Trumpism mean we know when they come and when they fall in theory and in practice?
What do you think?
You have seen the comings and goings now of Trumpism, Brazilianism, and Brexism, 2016 to 2024 and the common theme is why they failed to persist in power ONCE THEY CAME TO POWER.
If you look at the evolution of democracy theory since 2016 paradigm shift from normal to extreme liberal democracies in some countries you and you adjusted your previous democratic thinking as now EFFECTIVE TARGETED CHAOS and THE NATURE OF THE COURT SYSTEM IN A CONJUNCTURAL CAUSALITY MODE play a key role.
If you take into account this, then you may be able to see that the necessary and sufficient conditions for normal liberal democratic outcomes to come to exist and persist has changed as conditions have changed.
And this raises the question: What is the necessary and sufficient condition for normal democratic outcomes to maintain power regardless of the coming and going of exism movements and dictatorship threats?
What do you think the necessary and sufficient condition is?
Note: The answer is short.
Hello dears.
In my research thesis I need use a holistic view method such as 2 dimensions phase space , 3 dimensions phase space or maps such chirikov map , logistics map and... With matching deep Neural networks for Exploring Brain Dynamic via EEG in music composition.
Please guide me about some things.
1.which features better I extraction? & How?
2.which neural networks you prefer?
3.this is a good topic for thesis?
Thank you so much for help and support.
There was widespread social discontent/protest in the UK in 2016 after Brexit/2016 and in the USA after Trump/2016 after their exism movements won the democratic contest under effective targeted chaos.
The same has happened in other countries where liberal democracies under majority rule have produced an extreme democratic outcome since 2016, the latest case is ARGENTINEXISM/2023.
And this raises the question: Murphy's law remorse and widespread social protest/discontent after exism movements/extreme democratic outcomes come in to power: Are they linked?.
What do you think?
If you think that they are linked why do you think so?
If you think they are not linked why do you think so?
Note:
Key concepts: Murphy's law, Murphy's law remorse, effective targeted chaos, exism movements, extreme democratic outcomes, social discontent after the fact
In the late 1990s, neuroscientists announced the discovery of the "God spot" in the brain, located in the temporal lobe, just behind the temples. This neural cluster encourages us to ask fundamental questions, seek fundamental answers about the meaning of existence, strive for higher purposes, and dream of better tomorrows etc. It becomes active when we feel love, peace, beauty, true faith...Has the scientific existence of spiritual intelligence been proven, and if so, what role does the dozy chaos play in it?
If you are a researcher working with chaos and chaotic systems, which unsolved problem or question you have in mind
Here I have collected some open problems and questions related to chaos and chaotic systems for anyone interested. Most of them are borrowed from Professor J. C. Sprott.
Do you have anything more to add?
Best Regards,
Sajad
1. Can we mathematically prove that the system Sprott A (see file 01) is conservative? It has many coexisting nested tori and one chaotic sea. Some hints can be found in file 02.
2. See file 03. Can we have a better model that results in more similarity between figure 5 and figure 4?
3. Find the algebraically simplest example of an attracting 2-torus in a three-dimensional autonomous system of ordinary differential equations.
4. A common problem is to find a mathematical model that mimics the apparently chaotic dynamics of an experimental system. Models that give good short-term predictability tend to give very inaccurate long-term behavior, even to the point of having unbounded or non-chaotic solutions. Is it possible to find models of data that give the right topology of their strange attractor at the expense of short-term predictability?
5. Under some conditions (such as for the Hénon map) the boundary of the basin of attraction is smooth, and under other conditions (such as for the Mandelbrot set) it is fractal. What conditions determine the shape and size of the basin of attraction? Is there a correlation of its fractal dimension with the dimension of the attractor or other quantity? What role do the Cauchy-Reimann equations play, if any? Can two-dimensional maps that satisfy the Cauchy-Reimann equations have chaos on a set of nonzero measure in their parameter space?
6. Power spectrum analysis is not very useful for distinguishing chaos from noise since it appears possible to construct a chaotic system that produces an arbitrary power spectrum. For that purpose, people rely on the correlation dimension (Grassberger and Pracaccia, Phys. Rev. Lett. 50, 346-349 (1983)). However, Osborne & Provenzale (Physica D 35, 357, 1989) have shown that colored noise can give a spuriously low correlation dimension. Can it be shown analytically or numerically that an appropriately chosen noise spectrum can produce the same correlation integral as an arbitrary chaotic system?
7. Some earlier work indicates that the probability that a polynomial map with arbitrarily chosen coefficients is chaotic decreases with the dimension of the map. This result is counterintuitive and contradicts results for polynomial flows and for discrete-time neural networks. What is the reason for the different behavior?
Dear colleagues at first assumed that we have one chaotic system and in this system strange attractor so How can i find basin of attraction of it.
can you introduce some sources about it?
thanks
COMPLEXITY IN SCIENCE, PHILOSOPHY, AND CONSCIOUSNESS:
DIFFERENCES AND IMPORTANCE
Raphael Neelamkavil, Ph.D., Dr. phil.
1. Introduction
With an introductory apology for repeating a few definitions in various arguments here below and justifying the same as necessary for clarity, I begin to differentiate between the foundations of the concept of complexity in the physical sciences and in philosophy. I reach the conclusion as to what in the concept of complexity is problematic, because the complexity in physical and biological processes may not be differentiable in terms of complexity alone.
Thereafter I build a concept much different from complexity for application in the development of brains, minds, consciousness etc. I find it a fine way of saving causation, freedom, the development of the mental, and perhaps even the essential aspects of the human and religious dimension in minds.
Concepts of complexity considered in the sciences are usually taken in general as a matter of our inability to achieve measuremental differentiation between certain layers of measurementally integrated events within a process or set of processes and the same sort of measurementally integrated activities within another process or set of processes.
But here there is an epistemological defect: We do not get every physical event and every aspect of one physical event to measure. We have just a layer of the object’s total events for us to attempt to measure. This is almost always forgotten by any scientist doing complexity science. One tends to generalize the results for the case of the whole object! Complexity in the sciences is not at all a concept exactly of measurement of complexity in one whole physically existent process within itself or a set of processes within themselves.
First, what is termed as complexity in an entity is only the measure of our inability to achieve measurements of that part of a layer of process which has been measured or attempted to be measured. Secondly, always there is a measuremental comparison in the sciences in order to fix the measure of complexity in the aspects that are measured or attempted to measure. This is evidently a wrong sort of concept.
The essential difference here must be sharpened further. As a result of what is said above, the following seems more appropriate. Instead of being a measure of the complexities of one or a set of processes, complexity in science is a concept of the difference between (1) our achieved abilities and inabilities to achieve the measurement of actual complexity of certain levels of one physical process or a set of processes and (2) other types of levels of the extent of our ability and inability to measurement within another process or set of processes. This is strange with respect to the claims being made of complexity of whichever physical process a science considers to measure the complexity.
If a scientist had a genuine measurement of complexity, one would not have called it complexity. We have no knowledge of a higher or highest complexity to compare a less intense complexity with. In all cases of complexity science, what we have are just comparisons with either more or less intense complexities. This makes the concept of complexity very complex to deal with.
2. Is Complexity Really Irreducible?
On a neutral note, each existent physical process should possess great complexity. How much? We do not know exactly; but we know exactly that it is neither infinite nor zero. This truth is the Wisdom of complexity. Let us call it complexity philosophy. This philosophical concept of complexity within the thing itself (CI) is different from the methodologically measurement-based concept of complexity (CM) in the sciences. In CM, only the measured and measurable parts of complexity are taken into consideration and the rest of the aspects and parts of the existent physical process under consideration are forgotten.
If this were not true, the one who proposes this is bound to prove that all the aspects and parts of the physical process or at least of the little layer of it under measurement are already under any one or more or all measurementally empirical procedures with respect to or in terms of that layer of the process.
To explain the same differently, the grade of complexity in the sciences is the name of the difference (i.e., in terms of ‘more’ or ‘less’) between the grades of difficulty and ease of measuring a specific layer of causal activity within one process and a comparable or non-comparable layer of causal activity in another.
Both must be measured in terms of the phenomena received from them and the data created of them. Naturally, these have been found to be too complex to measure well enough, because we do not directly measure, but instead measure in terms of scales based on other more basic scales, phenomena, and data. But the measure-elements titled infinite-finite-zero are slightly more liberated of the directly empirically bound notions. I anticipate some arguing that even these are empirically bound. I am fully agreed. The standpoint from which I called the former as formed out of directly empirically bound notions is different, that is all.
Both the above (the grades of difficulty and ease of measuring a specific layer of causal activity within one process and a comparable or non-comparable layer of causal activity in another) must be measured in terms of certain modes of physical phenomena and certain scales set for these purposes. But this is not the case about the scale of infinity-finitude-zero, out of which we can eternally choose finitude for the measure of ease and difficulty of measuring a specific layer of causal activity without reference to any other.
The measure-difference between the causal activities is not the complexity, nor is it available to be termed so. Instead, complexity is the difference between (1) the ease and difficulty of measuring the one from within the phenomena issuing from certain layers of the physical process and the data created by us out of the phenomena, and (2) the ease and difficulties of measuring the same in the other.
In any case, this measure-difference of ease and difficulty with respect to the respective layers of the processes can naturally be only of certain layers of activity within the processes, and not of all the layers and kinds of activity in them both. Evidently, in the absence of scale-based comparison, their complexity cannot be termed a high or a low complexity considered within itself. Each such must be compared with at least another such measurementally determined layer/s of process in another system.
3. Extent of Complexity outside and within Complexity
The question arises now as to whether any process under complexity inquiry has other layers of activity arising from within themselves and from within the layers themselves from which directly the phenomena have issued and have generated the data within the bodily, conscious, and cognitive system of the subjects and their instruments.
Here the only possible answer is that there is an infinite number of such layers in any finite-content physical processual entity, and within any layer of a process we can find infinite other sub-layers, and between the layers and sub-layers there are finite causal connections, because every existent has parts that are in Extension and Change.
The infinite number of such complexity layers are each arrangeable in a scale of decremental content-strength in such a way that no finite-content process computes up to infinite content-strength. This does not mean that there are no actual differences between any two processes in the complexity of their layers of activity, or in the total activity in each of them.
Again, what I attempt to suggest here is that the measured complexity of anything or of any layer of anything is just a scale-based comparison of the extent of our capacity to discover all the complexity within one process or layer of process, as compared to the same in another process or layer of process.
4. Possible Generalizations of Complexity
Any generalization of processes in themselves concerning their complexity proper (i.e., the extent of our capacity to discover all the complexity within one process or one layer of activities of a process) must now be concluded to be in possession of only the quantitative qualities that never consist of a specific or fixed scale-based number, because the comparison is on a range-scale of ‘more than’ and ‘less than’.
This generalization is what we may at the most be able to identify regarding the complexity within any specific process without any measuremental comparison with another or many others. Non-measuremental comparison is therefore easier and truer in the general sense; and measuremental comparison is more applicable in cases of technical and technological achievements.
The latter need not be truer than the former, if we accept that what is truer must be more general than specific. Even what is said merely of one processual object must somehow be applicable to anything that is of the same nature as the specific processual object. Otherwise, it cannot be a generalizable truth. For this reason, the former seems to be truer than the latter.
Now there are only three possibilities for the said sort of more general truth on comparative complexity: accepting the infinite-finite-zero values as the only well-decidable values. I have called them the Maximal-Medial-Minimal (MMM) values in my work of 2018, namely, Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology.
Seen from this viewpoint, everything physically existent has great processual-structural complexity, and this is neither infinite nor zero, but merely finite – and impossible to calculate exactly or even at any satisfactory exactitude within a pre-set scale, because (1) the layers of a process that we attempt to compute is but a mere portion of the process as such, (2) each part of each layer has an infinite number of near-infinitesimal parts, and (3) we are not in a position to get at much depths and breadths into all of these at any time.
Hence, the two rationally insufficient conclusions are:
(1) The narrowly empirical-phenomenologically measuremental, thus empirically partially objective, and simultaneously empirically sufficiently subjective amount of complexity (i.e., the extent of our capacity and incapacity to discover all the complexity) in any process by use of a scale-level comparison of two or more processes.
(2) The complexity of entities without having to speak about their existence in every part in Extension-Change and the consequently evident Universal Causality.
These are the empirically highly insulated, physical-ontologically insufficiently realistic sort of concept of complexity that the sciences entertain and can entertain. Note that this does not contradict or decry technological successes by use of scientific truths. But claiming them to be higher truths on complexity than philosophical truths is unjustifiable.
Now the following question is clearly answerable. What is meant by the amount of complexity that any existent physical process can have in itself? The only possible answer would be that of MMM, i.e., that the complexity within any specific thing is not a comparative affair within the world, but only determinable by comparing the complexity in physical processes with that in the infinitely active and infinitely stable Entity (if it exists) and the lack of complexity in the zero-activity and zero-stability sort of pure vacuum. It can also be made based on a pre-set or conventionalized arithmetic scale, but such cannot give the highest possible truth probability, even if it is called “scientific”.
MMM is the most realistic generalization beyond the various limit possibilities of scale-controlled quantities of our incapacity to determine the amount of complexity in any layer of processes, and without incurring exact numbers, qualifications, etc. The moment a clear measuremental comparison and pinning up the quantity is settled for, it becomes a mere scientific statement without the generality that the MMM realism offers.
Nonetheless, measuremental studies have their relevance in respect of their effects in specific technological and technical circumstances. But it must be remembered that the application of such notions is not directly onto the whole reality of the object set/s or to Reality-in-total, but instead, only to certain layers of the object set/s. Truths at that level do not have long life, as is clear from the history of the sciences and the philosophies that have constantly attempted to limit philosophy with the methods of the sciences.
5. Defining Complexity Closely
Consider any existent process in the cosmos. It is in a state of finite activity. Every part of a finite-content process has activity in every one of its near-infinitesimal parts. This state of having activity within is complexity. In general, this is the concept of complexity. It is not merely the extent of our inability to measure the complexity in anything in an empirical manner.
Every process taken in itself has a finite number of smaller, finite, parts. The parts spoken of here are completely processual. Nothing remains in existence if a part of it is without Extension or without Change. An existent part with finite Extension and Change together is a unit process when the cause part and the effect part are considered as the aspects or parts of the part in question.
Every part of a part has parts making every part capable of being a unit process and in possession of inner movements of extended parts, all of which are in process. This is what I term complexity. Everything in the cosmos is complex. We cannot determine the level of complexity beyond the generalized claim that complexity is normally limited within infinite or finite or zero, and that physical and biological processes in the cosmos come within the finitude-limit.
Hereby is suggested also the necessity of combining the philosophical truth about complexity and the scientific concept of the same for augmentation of theoretical and empirical-scientific achievements in the future. While determining scientifically the various natures and qualities of complexity, chaos, threshold states, etc. in a manner not connected to the philosophical concept of it based on the MMM method of commitment access to values of content and their major pertinents, then, scientific research will remain at an elementary level – although the present theoretical, experimental, and technological successes may have been unimaginably grand. Empirical advancement must be based on the theoretical.
Constant effort to differentiate anything from anything else strongly, by making differentiations between two or more processes and the procedures around them, is very much part of scientific research. In the procedural thrust and stress related to these, the science of complexity (and all other sciences, sub-sciences, etc.) suffer from the lack of ontological commitment to the existence of the processes in Extension-Change and Universal Causality.
The merely scientific attitude is due to a stark deficit of the most general and deepest possible Categories that can pertain to them, especially to Extension-Change and Universal Causality. Without these, the scientist will tend to work with isolated and specifically determined causal processes and identify the rest as non-causal, statistically causal, or a-causal!
6. Complexity in Consciousness
The above discussion shows that the common concept of complexity is not the foundation on which biological evolution, growth of consciousness, etc. can directly be based. I have plans to suggest a new concept.
Bibliography
(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.
(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.
(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.
(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.
(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.
I'm working on a many-unit model that shows a deterministic phase transition driven by a control parameter that do not contain noise or disorder, and drives the system to chaos basically, but at the same time an order parameter that shows a second order phase transition, and the system shows critical slowing down and power laws, percolation etc etc...many phase transition related features, but it is all deterministic so..I'm looking for references in this sense....I've found something similar only in cellular automatas....
Research the synchronization of chaos in an open feedback system and show the results through a program Matlab
Need of Spritual Upliftment is growing worldwide nowadays amid the chaos, disorder, violence, hatred, envity, and what not, around the world. There is high need of spritual education. Please enlighten if there are such studies going on anywhere. Don't forget to share with me.
Thank you in anticipation.
With warm regards,
Vidyanand
Hegel's Science of Logic involves a trinary process: understanding -> dialectical reasoning -> speculative reasoning -> understanding at a higher level. This is analogous to a period 3 orbit, a return to self mediated by the other A -> B -> C -> A.
A direct consequence of a really strange theorem in dynamical systems due to Sharkovskii is that for any continuous function on the reals f: R -> R, if f has an orbit of minimal period 3 then it has orbits of any minimal period (because 3 is the first number in the Sharkovskii ordering). This happens in particular for certain values of lambda for the logistic map, exhibiting the phenomenon of 'chaos'.
The graph of successive higher iterations of the logistic map exhibit self-similarity, a fractal-like nature. This again mirrors the structure of the logic in which each part is similar in its trinary structure to that of the whole, i.e. Being -> Essence -> Notion, but in Being we have Quantity -> Quality -> Measure. In Concept we have Subjective Notion -> Objective Notion -> Absolute Notion. At a further finer level inside Quantity we have for instance Pure Being -> Nothing -> Becoming, etc.
While traditional science deals with supposedly predictable phenomena such as gravity, electricity or chemical reactions, there is also Chaos Theory which deals with non-linear things that are virtually impossible to predict or control, such as turbulence, weather, the stock market, our brain states and so on.
When there is an earthquake there are too many unpredictable - unpredictable chaos factors in the behavior of the ground and the structure that change the stress measure of each individual structure.
Low-rise structure, mid-rise structure and high-rise structure react differently to the multiple frequencies of ground displacement reaching below the structure.
The direction of the earthquake is unknown, the ground acceleration reaching under the structure and determining the force of the earthquake is unknown, the exact content of the seismic excitation frequencies is unknown, the duration of the earthquake is unknown, a structure can withstand high acceleration for a short duration or low acceleration for a long duration, but cannot withstand high acceleration for a long duration, the magnitude of the earthquake is unknown, the distance from the epicentre of the earthquake to the structure is unknown, the focal depth of the earthquake is unknown, the composition of the ground between the structure and the earthquake which transmits the energy of the earthquake is unknown, e.g. e.g. soft soil increases ground displacement four to five times compared to rock. Even the maximum possible accelerations given by seismologists, which determine the seismic design factor, have a probability of being exceeded by more than 10%.
The correlation of quantities such as "inertia stresses, damping forces, elastic forces, dynamic characteristics of the structure, soil-structure interaction, imposed ground motion" is non-linear and by interacting with each other they change the behaviour and stress of the building.
I am engaged in applied research of seismic structures trying to eliminate and control all these unstable chaos factors lying on the ground and better construction by applying prestressing at the ends of the wall sections in order to reduce the deformation of their frame and increase the strength of their reinforced concrete without admixtures and mass increase which incidentally increases the inertia loads, and on the other hand I am embedding the structure with the ground for the first time in the world in order to rotate the inertia loads into the ground allowing the ground to participate in the response of the structure to the seismic displacements, excessively controlling the chaos of all these unstable factors, while increasing the quality of the foundation soil.
In addition to the above mentioned too, there are three other factors that I exploit to increase the earthquake carrying capacity of structures.
1) I built additional seismic damping mechanisms throughout the height of the building.
2) Decoupling of the elastic columns and beams and plates, from the rigid longitudinal prestressed and butted walls with the ground, allows them to collide with each other at the height of the diaphragms and in this way to cancel out the displacements of the load-bearing structure and the deformations.
3) I exploited the double lever arm of height and width of the longitudinal walls, so that the lever arm of width cancels out the torque tensions that the lever arm of height lowers at the base.
As researchers, we often immerse ourselves in the world of academia, but let us not forget the stark disparities that exist beyond our ivory towers. In Gaza and Israel, lives are marred by chaos, loss, and the relentless struggle for survival.
As our streets sparkle with festive lights, we must pause and recognize that elsewhere, every fleeting moment is a precious gift. In the midst of conflict and tragedy, the fragility of human life becomes painfully evident.
This discussion beckons us to reflect on the profound human cost of these ongoing events. Let us delve into the ethical, political, and social dimensions, contemplating how our academic roles intersect with the world's most pressing issues. How can we, as researchers and academics, become agents of positive change in a world yearning for peace?
Together, let us harness our collective knowledge to illuminate these critical concerns and labor towards a future where every life is cherished, and every voice is heard!
Hello everyone,
I would like to ask a question about particle scaling.
I have the particle size distribution data of crushed sand particles. However, the fragment size is too small which will significantly influence the computational efficiency. Therefore, I scaled up the fragment size and used BPM to model a sand particle with a diameter of 1.5mm (D50). After I had done it, the time step was still small (10^-9 s).
Considering the critical time-step is dependent on the smallest mass and stiffness, so then I scaled the stiffness and density, and then the time step increased to 10^-7 s.
But this would change its mechanical response behaviour. I would like to ask if there is any way to scale including fragment size, material properties such as mass and stiffness, and be able to make the mechanical behaviour of modeled particles close to the behaviour of real sand.
Kind regards,
Chao
Hello, everyone!
I recently got the problem of calculating Friedif(obs) through SXRD intensity data. I tried several ways to calculate it, but failed. The results I calculated turned out to be total chaos.
Accidentally, I found Platon could analyze Bijvoet Pairs. There were Friedif (both stat and obs). Therefore, I was wondering if these results were correct? Or is there any methods to calculate Friedif(obs) through SXRD intensity data?
Could anyone please give me any advice or help me explain this?
Thanks in advance.
By looking at daily news bulletins, the lack of a supreme central authority, the prevalence of coups around the world, and the chaos in societies, what is its cause?
In my opinion, the perceptron and other machine learning algorithms can evaluate quite complex functional dependencies of time series, if you have any ideas for further research in this vein, welcome to a private or public discussion.
The study presents a bio-inspired chaos sensor model based on the perceptron neural network for the estimation of entropy of spike train in neurodynamic systems.
Dear colleagues
To find coexisting attractors in a chaotic system, I use the continuation diagram. Here in each iteration, the initial conditions x(0) for the chaotic system are set as the final conditions x(t_final) from the previous simulation.
We do so as we increase the parameter under study (forward continuation diagram), and as we decrease the parameter (backward continuation diagram).
In a system I am studying though, I still know that coexisting attractors exist, and using both continuation diagrams, I still cannot depict all of them. The diagram cannot 'catch' them.
Is there an alternative, or a solution to this?
According to the principal of entropy increase, it's easier to form more disordered crystal strcuture at low temperature. Do I mixed up the concepts of chaos and disorder?
"The word (concept) art, science, and engineering are closely related" contains over fifty innovative keys. Moreover, every creative key adds new information and knowledge to art, science, and engineering concepts.
What is the unified and stable science of the word?
This question raises other questions, and one of them resulted in a new science called the science of the unified word by Fayad
To learn this, we must find definitive answers to the following questions.
Please answer the following questions:
What is the word classification?
What is the common purpose of any word?
What is the impact of the unified goal of any word?
What is the chaos of any word?
What are the reliable sources for any word?
What is the responsibility of the word?
What is the philosophy of any word?
What roles does the wordplay?
What is the collaboration of the word?
What are the characteristics of the word?
What is the behavior of the word?
What is the code of honor for the word?
What is the knowledge of the word?
What is the knowledge map of the word?
What is the logic of the word?
What is the interpretation of any word?
What s the rules of the words?
and others
I want to find eigen frequencies of a cantilever beam. The beam has random elastic modulus. The stiffness matrix is obtained using kosambi karhunen loeve method as A_0+A_i. where A_o is mean stifness matrix and A_i is fuction of normal random variable. The egien values are expanded in terms of polynomial chaos expansion. The final equation is obtained after galerkin projection. The equation is attached in the files. I want a matlab code to obtain the the eigen frequencies,
Hello,
I would like to ask a question about how particle position affects torque.
In the DEM simulation, basically is apply the normal load to the upper rigid body, bring the upper rigid body and lower rigid body together, and then apply the angular velocity to the lower rigid body, these two rigid body twist against each other.
An annular contact surface is formed when two rigid bodies are in contact, and then spherical particles are applied to the contact area. I found that if all particles are placed on one side, the measured torque is large, while if the particles are on both sides or evenly distributed in the annular contact area, the measured torque becomes smaller.
So, I was wondering whether a relationship exists between particle position on the contact area and torque.
Could you please share your ideas or provide any references?
Many thank,
Chao
we know that the standard logistic map x(n+1)=px(n)(1-x(n)) has equilibrium points x=0 and x=(p-1)/p.
What are the equilibrium points of the caputo fractional order version of this equation?
Is it x=0 and x=1 or x=0 and x=(p-1)/p?
According to study "Wu, G.C., Baleanu, D.: Discrete fractional logistic map and its chaos. Nonlinear Dyn. 75, 283–287 (2014)" equilibrium points are x=0 and x=1, but in the study "Comments on “Discrete fractional logistic map and its chaos” [Nonlinear Dyn. 75, 283–287 (2014)]" equilibrium points are x=0 and x=(p-1)/p.
It is possible to find many different applications like this in the literature.
Does anyone have a satisfactory explanation for this issue?
Dear colleagues
When computing the Fuzzy Entropy measure, most works use an Exponential fuzzy function. Yet, there are two deviations between the works.
Some use the term
exp(-dij^n/r)
so the power 'n' goes to the numerator only, while other works use
exp(-(dij/r)^n)
so the power 'n' goes to the whole fraction.
Which one is the correct?
Relevant works are the following, where the issue appears
--Chen, W., Wang, Z., Xie, H., & Yu, W. (2007). Characterization of surface EMG signal based on fuzzy entropy. IEEE Transactions on neural systems and rehabilitation engineering, 15(2), 266-272.
--Chen, W., Zhuang, J., Yu, W., & Wang, Z. (2009). Measuring complexity using fuzzyen, apen, and sampen. Medical engineering & physics, 31(1), 61-68.
--Azami, H., Li, P., Arnold, S. E., Escudero, J., & Humeau-Heurtier, A. (2019). Fuzzy entropy metrics for the analysis of biomedical signals: Assessment and comparison. IEEE Access, 7, 104833-104847.
--Xiang, J., Li, C., Li, H., Cao, R., Wang, B., Han, X., & Chen, J. (2015). The detection of epileptic seizure signals based on fuzzy entropy. Journal of neuroscience methods, 243, 18-25.
Dears,
I am interested in chaotic behavior in classical biological models to spread any disease.
To the best of my knowledge, I do not be able to find references that analyzed possible chaotic behavior in models like SEIR, SEVAIR, or others.
Please, if you know of any papers about chaos and classical models in Epidemiology, I would like to know this research.
Regards,
Luciano.
These values are:
** Description. Some social schollars point that it is a low level critical thinking or low cognitive function. Yet, to describe a phenomenon in physics, objectively and realistically, it is worth a Nobel sometimes. Now i think it is not a non transfersble skill in education/learning research, though phenom there are defined differently or non central
** Explanation. Again, the same reasoning. Explanation to phenomena, weird unexpected to observed effect (as they are, of specific status) are valuable, meaning-fulfilling to our drive to make order in the chaos of world and this dignificant. Now if explanation is low on Bloom or Bigg's scale it cannot undermine the level of that thinking function or skill
** Predictions. These are high in both Positivist and non Positivist realms but non available in non Positivist bc of non priority or causal sequences deprioritization
In the end, is science is undermined in the eye of social schollars due to.. ignorance?
Many times while dealing with ecological models, we come across the phenomena of chaos, and while making bifurcation diagrams with respect to a bifurcation parameter, sometimes system becomes chaotic then periodic again becomes chaotic and so on. My main queries are like:
1. What is ecological significance of chaos in a dynamical system.
2. What is ecological significance of this type of stability change in a dynamical system (chaos-periodic-chaos...)?
Dear Colleagues,
Thanks for your prompt responses. But if we plot bifurcation diagram, lypanuov exponent and tragectory plot for function rx(2-3x) it shows different behaviour. So, it attracted my attention to do work on it. The bifurcation diagram of rx(2-3x) suggests that there is no bifurcation but only a little discrete chaos has rate of convergence good as compared with logistic map. If anyone interested in doing work on this new scheme, please send me the email through which we can communicate and whatsapp number also, so that frequency of interaction shall be increased and neck to neck traversing of results can be made jointly.
Manish
Nowadays, AI and Machine Learning are dynamic field in Computer Science. Many researchers are doing the research in the mentioned field. How the chaos technique are connected in the mentioned field. Is there any research papers are published before.
The value of Lyapnov exponent is found using Wolf algorithm for step size of 0.01 and observation time of 10^5 in MATLAB 2020 using ode45 solver.
It is well-know that the Poincaré - Bendixon theorem eliminates dynamical chaos in 2d continuous, autonomous systems on plane, or sphere, or cylinder. However, for systems on 2d torus one new possibility appears: the trajectory can twist along the torus sweeping the entire torus. Can we state that in this case such systems do not have sensitive dependence on initial conditions (i.e. the Lyapunov exponents tend to 0)?
Intuitively, I think that it is indeed that case. My suggestion is based on an analogy to the linear case. Imagine the system of two angles which linearly increase with two irrational frequencies. If we put this system on the torus, then the trajectory will sweep all the torus, but the Lyapunov exponent will be 0.
The positive Lyapunov exponent confirms chaos is a bounded, deterministic system. I suppose the boundedness of the system has to comply with the presence of one zero Lyapunov exponent. Then again why zero? Why not negative? It will be very helpful if I get a deeper insight here.
Though it has been a few decades since Chaos Theory made its way into Economics and Finance through the works of Baumol & Benhabib, Alison Butler, David Levy, Philip Mirowski, Michael McKenzie, Robert Gilmore and Blake LeBaron
(among others), it is observed that most of the mainstream economics and finance journals are reserved towards publishing empirical papers on chaos in financial markets. Publications to this end are very few and most of them are published in a handful of journals.
As I am looking forward to write empirical papers examining the evidence of chaos in commodity markets, I wish to know the odds of my work seeing the light of the day. Any useful suggestion/information in this regard would be highly appreciated.
I am currently working on the interrelatedness between the self and identity.
How is the self connected to identity? Can we talk about the self as a form of identity?
I am also working on the development of the self amid disease and pandemics.
What effects do pandemics and diseases have on the self?
Your views and opinions are welcome.
The Literature review on the matter is also most welcome.
Thank you
As there are three state variable(x,y,z)
I want to train EEG data using rosller attracttor.
2 Logistic chaotic sequences generation, we are generating two y sequence(Y1,Y2) to encrypt a data
2D logistic chaotic sequence, we are generating x and y sequence to encrypt a data
whether the above statement is correct, kindly help in this and kindly share the relevant paper if possible
I was recently recieved the first decision of my submitted paper on Advanced Functional Materials. The editor gave the following comments:
Statistics: For original research, please check that your manuscript includes a sub-section entitled "Statistical Analysis" at the end of the Experimental Section that fully describes the following information:
1. Pre-processing of data (e.g., transformation, normalization, evaluation of outliers),
2. Data presentation (e.g., mean ± SD),
3. Sample size (n) for each statistical analysis,
4. Statistical methods used to assess significant differences with sufficient details (e.g., name of the statistical test including one- or two-sided testing, testing level (i.e., alpha value, P value), if applicable post-hoc test or any alpha adjustment, validity of any assumptions made for the chosen test),
5. Software used for statistical analysis.
Does anyone has experience recieving these comments? I wonder whether all of the research articles are needed to illustrate this statistical analysis details? I saw most of the published paper of AFM don't have this section. So can anyone give me some advice?
Thank you
Chao
I am currently working on the interrelatedness between the self and identity.
How is the self connected to identity? Can we talk about the self as a form of identity?
I am also working on the development of the self amid disease and pandemics.
What effects do pandemics and diseases have on the self?
Your views and opinions are welcome.
The Literature review on the matter is also most welcome.
Thank you
Literature review about the self and identity, the development of the self amid disease and chaos
Chaos leads to order, but can entropy be stopped? Please explain if you can find the time.
I want to investigate some countries covid data with simulation for the following situations.
1. to identify the effect of covid in financial crisis
2. spreading versus market risk etc.
Using MATLAB, how to draw the bifurcation diagram for a chaotic system?
Can you kindly share any *.m file (MATLAB code) for this? How to do this?
Can you illustrate the bifurcation analysis with any classical system like for example, the Lorenz system?
Hello everyone,
Strange Nonchaotic Attractors are known as a rather new class of attractors that, despite having fractional dimensions, do not illustrate chaos in the conventional sense (exponential divergence of infinitesimally close trajectories and positive Lyapunov exponents). I have some questions about this class of attractors and their properties.
1. Is the response of the SNAs without any period? (so if we look at them, we cannot predict where EXACTLY the trajectory will be in time T, where T is a positive value).
2. Are SNAs the same as weakly chaotic systems? because I've encountered systems that illustrate non-exponential divergence but due to a lack of periodicity, are called weakly chaotic. If they are different, what is the distinction?
3. Chaotic attractors are known to have a positive, a negative, and a zero Lyapunov exponent. What are the Lyapunov exponents of SNAs?
4. If one uses the idea of Poincare maps to analyze SNAs, how the results will differ from the results of chaotic attractors?
Since we know that the Lyapunov exponent is the exponential measure of the separation between infinitesimally close phase-space trajectories. One positive exponent specifies the presence of chaos in the solutions of the dynamical system. When there are two positive exponents then the hyper-chaos can be observed in the system. Now, is it possible for a system to have more than two positive Lyapunov exponents? If yes, how that system will behave?
Thanks in advance for your help in this regard.
It is known that imaginary potentials are a source of particles when included into the Gross-Pitaevskii equation. As far as the dynamics of a Bose gas is concerned, is it possible that these potentials could be a source for chaos? Did anyone investigate this before?
I have two simulations of periodic plane channel flow using scale resolving simulation, one with large turbulent structures and later with small turbulent structures (more chaos). Whenever I am analyzing instantaneous velocities from both the cases, I cannot see much difference between the Kolmogorov Spectrum. Can someone explain how turbulent intensity scales with Kolmogorov Spectrum.
Thank you.
The Van der Pol oscillator can be give in state model form as follows:
dx/dt = y
dy/dt = mu (1 - x^2) y - x,
where mu is a scalar parameter.
When mu = 0, the Van der Pol oscillator has simple harmonic motion. Its behavior is well-known.
When mu > 0, the Van der Pol oscillator has a stable limit cycle (with Hopf bifurcation).
While we can show the existence of a stable limit cycle with a MATLAB / SCILAB plot with some initial conditions and some positive value for mu like mu = 0.1 or 0.5 (for simulation), I like to know if there is a smart analytical proof (without any simulation) showing the existence of a limit cycle.
Specifically I like to know - is there any energy function V having time-derivative equal to zero along the trajectories of Van der Pol oscillator? Is there some smart calculation showing the existence of a stable limit cycle..
I am interested in knowing this - your help on my query is most welcome. Thanks!
Whether the existence of periodic window affects the encryption efficiency or not?
Business management (and operations) has many intertwined aspects, which constantly interact with each other, raising the complexity of it, as a 'system'. Modelling a complex system is difficult due to dependencies and adaptive behaviour. However, such complex 'systems' self-re-organise and become sustainable. A close-related concept of chaos indicates that a change in the initial conditions can bring out randomness, even with deterministic laws. Though the chaos and complexity theories are interrelated and multi-disciplinary in nature, very less application found in business management research.
The onset of Covid-19 pandemic has presented a unique social context for chaos and complexity.
Fellow scholars of this RG are requested to highlight:
a) recent trends in research in this area (how chaos is measured, analysed?).
b) recent applications of chaos and complexity theories in the field of business management
c) modelling techniques, related to chaos and complexity theories
Most populations of salmonids differ from each other in molecular genetics, morphology, life history, etc., with many populations showing local adaptations. While some populations, or groups of populations, meet the requirements for species designation under an integrative framework, to recognise all populations showing adaptive differences and distinct evolutionary trajectories as distinct species would result in taxonomic chaos. In North America important populations can be identified as Conservation Units (CUs) such as Evolutionarily Significant Units or Designatable Units within the appropriate conservation legislation. With a few exceptions, the CU approach does not appear to be widely used elsewhere, possibly due to difficulties with current legislation.
Effective conservation of trout and char should be based on populations, irrespective of whether they are designated as species, subspecies or simply populations, although CUs need to be rooted in accepted species. Each population can then be assessed as to its biological significance based on: genetic distinctness as determined by genomic techniques especially where this is of adaptive significance; genetically-based tolerance of extreme environmental conditions; unusual genetically-based life history traits; phylogenetics; distinct morphology where this has a genetic and adaptive basis; geographical isolation, especially where adjacent populations are extinct; lack of introgression from non-native conspecifics; occurrence as a member of an unusual or rare native species community; cultural, economic, and recreational importance. This biological significance taken together with potential threats to the population’s continued survival can be used to produce a priority ranking. Such a priority ranking can assist in allocating limited resources for conservation thus ensuring that this is carried out in a focused way.
Chaos is a long-term non-periodic behavior in a deterministic system that is dependent
Shows sensitivity to initial conditions.
The operating environment of chaos is dynamic systems. A dynamic system consists of a single phase space or a fuzzy state whose coordinates determine the dynamic state of the system using dynamic laws.
A dynamic system can be Intermittent or chaotic. Dynamic systems (Lorenz-Rossler) are called strange attractors because they are a set of all paths that converge toward a fixed point, a finite loop, or so on.
Attractors are highly sensitive to initial conditions and are called strange because they consist of a fractal set.
+1
As for example, existence of limit cycle oscillation means the existence of hopf-bifurcation. I am very keen to know the ecological significance of these terms rather than mathematical meaning. How can we relate these technical terms in real life?
Dear colleagues,
amazingly we are following the developments regarding COVID-19 and the worldwide havoc and chaos it caused.
Surely, everyone will be happy to see this pandemic coming to an end without causing more pain.
Those, who dedicated their time and efforts to find a solution for mankind need to be appreciated. In this sence, one of the first and at the same time, kind faces of the CEO of BionTech, Ugur Sahin and his partner/wife OzlemTureci are the best candidates for the next Nobelprice.
Do you agree with me ?
Best regards
Zehra
Hello
I am trying to optimize Soxhlet oil extraction using the Design of experiments and Response surface methodology. For the moments I have all the parameters that want to optimize (4 parameters and 2 responses) but I am a little bit confused about which type of design I will use because I do not know which criteria define this choise?
About 12000 B.C. was chaos. Agricultural era occurs about 10000 B.C. Period from 8000 B.C. to 4000 B.C. is a static era. From 4000 B.C. to 2000 B.C. appeared wheel, letter, patriarchy . From 2000 B.C. is the periodic era. About in the year 2000 A.D. is chaotic era (chaos theory). Is everything created from chaos and everything returns to chaos?
It is clearly that we live i chaotic world. As physicists say, chaos waits us everywhere, from the heartbeat to the universe. Unlike of the most problems in classic physic which are nonlinear, equitation of moving of quantum systems (like atoms and molecules) are linear. Since nonlinearity is a condition for the emergence of chaos, the question is: Is there quantum chaos?
I am new in the field of statistical analysis of microbial ecological data. I read many articles on microbial community structure and dynamics and data presentations varied. For shannon, simpson, Chaos means, some authors presented in a plot format and some cases presented in a table format. So I would like to know which one is better?
COVID-19 was a synonym of tragedy and chaos in the Northern Hemisphere. In Africa, however, even the common cold might be more serious. What is happening?
Universal biogenesis
Brain equation
Smile theory
Artificial persons
Spiral chaos
Sound of chaos
Hyperchaos
Cryodynamics sister of Thermodynamics
Augustinian cosmology, confirmed
Lampsacus Hometown
In everyday speech, chaos means disorder, crowd, unpredictability, etc. In philosophy, chaos is used in the terms of pro-matter, primordial space, that is, what became before order was brought into our world. In psychology, the word chaos raises fears that order will disappear and disorder will reign again. Chaos is a new field of science, but also a new way of observing the world. So, for physicists, engineers, economists, doctors, biologists, sociologist, psychologists, psychiatrists etc., chaos means an incentive to re-examine their equations, data, knowledge and beliefs. Chaos enabled a systematic approach to phenomena and systems of great internal complexity as well as an understanding of seemingly extremely simple phenomena. Many (but not all) scientists agree that after the theory of relativity and quantum physics, chaos is the third scientific revolution.Is theory of chaos the third scientific revolution?
- Universal biogenesis
- Brain equation
- Smile theory
- Artificial persons
- Spiral chaos
- Sound of chaos
- Hyperchaos
- Cryodynamics, sister of Thermodynamics
- Augustinian cosmology confirmed
- No finished black holes
- CERN proven risky
- Lampsacus Hometown as world democracy Dec. 11, 2020
Hi, How can we calculate the entropy of chaotic signals? Is there a simple method or formula for doing this?
Targeted chaos and misinformation are at the heart of extreme democratic outcomes as they are the active ingredients needed for them to come to exist, to persist, and to propagate. One example of extreme democratic outcome is USEXIT or Trumpism.
Targeted chaos and misinformation are mostly based on fake facts or an alternative facts, which raises the question “Are extreme democratic outcomes when in conflict and the rule of law in liberal democracies incompatible?
I think yes, what do you think? Why do you think so?
In the context of some ruling parties/persons/governments, it has been widely felt that they do deliberately fail to deliver economic prosperity. Instead of promoting economic development, they do opt for designed economic deceleration and widespread social vulnerability. They do create chaos to appropriate maximum political and economic value only to themselves.
Given that, what are the pros and cons of such a deliberately brought about economic crisis?
Can we study such a phenomenon? How?
Regards...
Hello,
I would like to compare the bending moment of a tube with beam and shell element in ansys? The tube has the same dimension in beam and shell element. In beam element, i can get the bending (My, Mz) and torsional(TQ) moment. But in the shell element, in the help of Ansys, I could only get the bending moment per length (M11, M22, M12) and Bending stress(Sb11, Sb22,12).
If i want compare the results of Mz in the beam element, How could I get the same "Mz" in the shell element?
Thanks
Chao REN
- Theory of chaos describes behaviour of dinamic systems evolution which are sensitive on starting conditions. Chaos implies nonlinearity. Nonlinear relationship are a necessary condition for chaotic systems. Existance of nonlinearity alone does not make a chaotic system. All natural processes are nonlinear. Human brain is the most chaotic system on world. Is chaos organisational form of nature?
I think the chaos applies to all theory because chaos existed in classical physics itself so the chaos should exists in quantum and relativity
Second Law of Thermodynamics states that as usable energy is lost, chaos increases - and that progression towards disorder can never be reversed.
Dear colleagues
I want to ask, where can I obtain the original versions of classic photos that are traditionally used for image encryption?
Examples include the Lenna figure, vegetables, baboon, cameraman, rice, etc.
Is there any source to get all such images, and maybe try out new ones, that aren't bound by any copyright.
Apart from the above, I want to see if there are any copyright free images of other types, like fingerprints, x-ray images, satelite images, that can be used as examples in image encryption papers.
Chaos theory is a delightful contradiction - a science of predicting the behavior of "inherently unpredictable" systems. It is a mathematical toolkit that allows us to extract beautifully ordered structures from a sea of chaos - a window into the complex functioning of natural systems as diverse as the beating of the human heart and the trajectories of asteroids. So, how can this theory explain a crisis situation in general, and that of the Covid-19 pandemic in particular?
Bifurcation diagrams are very useful to evaluate the dynamical behavior of nonlinear dynamical systems. In chaos literature, I notice that some authors draw bifurcation diagrams by removing the first 1000 seconds of data. I like to understand the reason behind this. Any help on this is highly appreciated. Thank you!
Wolf's and Rosenstein's algorithms does not seem to include the multidimensional scenario (if I understand them correctely). I want to measure the nonlinear dynamics of the liquid state machine's dynamical system.
Edward Lorenz, who became famous for the butterfly effect ( sensitive dependence of the system on initial conditions), long ago found that the mess is a secret agent of order. The Universe is one enormous randomness and a huge collapsing to complete disintegration. However, randomness that gets routed can produce incredible new complexity. God gambles with the Universe, says Joseph Ford, paraphrasing Albert Einstein's famous claim that God does not it. Is evolution a chaos with feedback?
Consider the famous fractal sets, Mandelbrot and Julia sets. They are based on the idea of choosing two complex numbers Z(0) and C with proper run time and escape-region. They are achieved by repeatedly evaluating the following equation:
Z(n+1) = Z(n)^2+C
For example, in Mandelbrot set, consider a 400×400 mesh when x is in [-2.5 1.5], y is in [-1.5 1.5], run-time is 32 and the escape region is 2.
The final plot is as follows
The yellow part in that figure corresponds to the points in which the value of the function never reaches the escape region. However, the different spectrum of the blue points corresponds to the iterations in which the function crosses the escape region
I have two questions:
a) Is there any study on the transient part of such process (and not steady state)
b) What happens when we don’t consider escape-region?
I developed a new cryptographic algorithm (block cipher) based on RADG and using chaos (tent Map) with key of 256 bit, the design of the RADG is no more fixed as it was, the design totally depends on the chaos seed X and TM parameter μ , which is vary .
I built the cipher/Decipher code and it works perfectly .
what standard test/validation programs should I use to prove validity ?
What do you think about chaos theory? In the discipline of international relations, we see that theories and paradigms such as realism, idealism and constructivism are often used to express international politics. The theory of chaos originating from science has been used in social sciences and international relations analysis in recent years. How can chaos theory work in global analysis?
One should never make self-propaganda – unless as a rational means to save all. I do therefore humbly apologize for my presenting the following list of highlights to you:
- Lawful chemical biogenesis [found when I was 20]
- Smile theory [enables a causal therapy for the physiological autism of mirror-competent bonding animals]
- Liquid automata
- Brain equation
- Spiral chaos - Hyperchaos - Generic Fractals
- Jumping identities between classical particles at invisible boundaries in position space [found when I was 40]
- Endophysics
- Global c, retrieved [the early Einstein, rehabilitated]
- Zwicky’s 1929 infinite eternal cosmos à la Saint Augustine, confirmed
- Cryodynamics, sister of deterministic Thermodynamics [found when I was 70]
- CERN camouflages its inability to renew its planetary safety report LSAG from early 2008, but continued and plans to continue further in the biggest crime of history
January 5, 2020
Our knowledge on Chaos theory is practically zero. Can anyone help us figuring out and explaining pattern of the chaos (please check out the figures only)
Preprint Chaos Theory Approximation
We have not found any research paper or textbook referring to this recurrence. Can you help us to explain these problems in terms of chaos theory?
Chaos exists not only in the mathematical world, but also in real life. From the quote: "All creativity begins in chaos, progresses in chaos and ends in chaos" ( Ralph Abraham), it follows that creating starts from chaos. Since the connection between imagination and creativity is obvious, can a direct connection be made between chaos and imagination?
If two interconnected boxes were to exchange water, Box#1 is full and Box#2 empty.
Suppose the rate of emptying of Box#1 is ½. It will generate a distribution 1, ½, ¼, 1/8, 1/16, … Let it be its probability distribution, p.
Similarly, the filling Box#2 will have a similar, filling of the box, distribution 0, ½, ¾, 7/8, 15/16, … Let us call it probability distribution q.
Information or Shannon entropy I(Box#1) = Sum of p ln(1/p) and I(Box#2) = Sum of q ln(1/q).
In our example of two interconnected, information sharing boxes, there will be
I(Box#1)> I(Box#2) always.
In the case of emptying @1/2, I(Box#1) =1.386 > I(Box#2) =0.8015.
The same is true for any other rate, like @1/4, I(Box#1) =3.45 > I(Box#2) = 2.165.
Or any other rate of transfer of water.
The question is: How can the information transferred between two interconnected, information sharing boxes be different while there is no ‘Channel’ in between? Can you answer? The clues are in the two references below. You can use any other reference of your choice, please explain this apparent PARADOX!
References: (1) C. E. Shannon, A Mathematical Theory of Communication, Bell Systems Tech. J. 27, 379 (1948). (2) S. Ahmad, Information generating, sharing and manipulating Source-Reservoir-Sink model of self-organizing dissipative structures, Chaos 28, 123125 (2018).
I really enjoyed Chaos by James Gleick. It's a popular-science-level text. But it got me interested in the area. What are some recommended books that are a step more advanced but still accessible to a novice in the field?
