Otto E. Rossler

• Dr. med., Dr. rer. nat. habil. professor
• Professor at University of Tübingen

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This issue is dedicated to the memory of Prof. Tenreiro Machado. https://dergipark.org.tr/en/pub/chaos/issue/64884

Chaos Theory and Applications (March 2022 - Volume 4 - Issue 1) https://dergipark.org.tr/en/pub/chaos/issue/63571 ----------- 1) Jun MA. "Chaos Theory and Applications：The Physical Evidence, Mechanism are Important in Chaotic Systems. " 2) Burak ARICIOĞLU, Sezgin KAÇAR. "Circuit Implementation and PRNG Applications of Time Delayed Lorenz System....

Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labeling. Addressing these problems corresponds to the development of a dynamical taxonomy, exhibiting the key...

Chaos Theory and Applications (November 2021 - Volume 3 - Issue 2) https://dergipark.org.tr/en/pub/chaos/issue/58077

Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine what are the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labelling. Addressing these problems correspond to the development of a dynamical taxonomy, exhibiting...

Chaos Theory and Applications (June 2021 - Volume 3 - Issue 1) https://dergipark.org.tr/tr/pub/chaos/issue/56378

Writing a history of a scientific theory is always difficult because it requires to focus on some key contributors and to “reconstruct” some supposed influences. In the 1970s, a new way of performing science under the name “chaos” emerged, combining the mathematics from the nonlinear dynamical systems theory and numerical simulations. To provide a...

https://dergipark.org.tr/en/pub/chaos ----- https://www.researchgate.net/project/Chaos-Theory-and-Applications-CHTA

Update on the 1974 paper containing the first and the 1981 paper containing the second description of the brain equation.

The design principle underlying Fig. 1.1 is easy to interpret in terms of realistic systems. The principle reads: ‘combine an oscillator with a switch and you are likely to obtain’.

Simple systems can produce complicated behavior. The reason lies in the structure of space and time. Simple ‘weaving rules’ suffice to determine very complicated motions.

The phenomenon of turbulence is, in a sense, too beautiful to be explained. It not only has infinite complexity—which is something we are accustomed to by now—but is non-repetitive in a much more creative way: it ‘draws’ a whole new flow pattern all the time.

If the presumable chaotic regime is low-dimensional and simple, the easiest thing to do is to prepare a next-amplitude map or some other one-dimensional projection of a cross section.

If complicated motions indeed occur so easily as has been suggest above, chaos should be among the ubiquitous phenomena of the world. This hypothesis seems not at variance with reality. To start out with a ‘far-fetched’ example, nonperiodically oscillating astronomical objects might be mentioned. Here the class of Cepheid pulsating stars is especia...

Lefschetz once remarked that Poincaré, after having discovered the possibility of homoclinic points, was well aware that from now on, the majority of simple dynamical systems could be expected to show the same complexity of behavior [1].

So far, a single design principle has proved sufficient to generate a whole world of nontrivial flows in three and higher dimensions. The resulting limiting equations appeared rather ‘robust’ in the sense that the limiting parameter \(\varepsilon \) could be increased from zero up to the order of unity (cf. Eq. ( 2.2)); and also in view of the fact...

As mentioned at the beginning, the reinjection is not confined to planar sub-systems. Reinjection processes between three-dimensional sub-systems, initiated along two-dimensional cross sections, are still quite easy to conceptualize and to generalize.

The oldest example of complicated behavior found in an unconstrained (non-conservative) dynamical system is, as mentioned in the Introduction, that found in the periodically forced van der Pol oscillator [1]. Cartwright and Littlewood’s results were based on painstaking analytical arguments (see the elaboration in [2]). Is it, at the same time, als...

Chaotic systems produce a characteristic noise, as described in Sect. 10.6. Does it suffice to diagnose chaos and, perhaps, also its higher forms?

Anaxagoras (see Introduction) inaugurated the philosophical hypothesis that a perfect mixture, existing since eons, could be unmixed. By adding the word ‘again’, we arrive at a mathematical version of the same conjecture. The deterministic maps of the preceding two sections are candidates examples. Even in its mathematical version, the conjecture h...

It would be astonishing if the just described ‘royal way’ to chaos was the only one. And it would also be astonishing if the next alternative—Lorenzian chaos—would not at the same time reveal a second principle — a whole second world.

Written in the 1980s by one of the fathers of chaos theory, Otto E. Rössler, the manuscript presented in this volume eventually never got published. Almost 40 years later, it remains astonishingly at the forefront of knowledge about chaos theory and many of the examples discussed have never been published elsewhere. The manuscript has now been edi...

The paper is a translation into English of a paper first published in German on the website of a newspaper. see: https://www.researchgate.net/post/Otto_E_Rossler_in_interview_with_an_anonymous_Interrogator --------------------------------------------------------------------------------------------------------------- https://www.tagblatt.de/Nachric...

The equivalence principle, Einstein's deepest thought from 1907, is based exclusively on specialrelativity with its global c. Yet Einstein reluctantly deduced from it as a formal implication that the speed of light c in the vacuum is reduced downstairs in his constantly accelerating long rocketship in outer space, and hence also in gravitation. Bec...

DOI: 10.13140/RG.2.2.31089.33126

Einstein's miraculous brainchild of the twins paradox is still worthy of consideration in the special context of gravitation. As shown in Kip Thorne et al.'s blockbuster movie "Interstellar," an astronaut who for a while has dwelt more or less deep down in the gravitational trough of a black hole can upon return be younger than his own daughter. Th...

The basic laws of deterministic many-body systems are summarized in the footsteps of the deterministic approach pioneered by Yakov Sinai. Two fundamental cases, repulsive and attractive, are distinguished. To facilitate comparison, long-range potentials are assumed both in the repulsive case and in the new attractive case. In Part I, thermodynamics...

Model validation from experimental data is an important and not trivial topic which is too often reduced to a simple visual inspection of the state portrait spanned by the variables of the system. Synchronization was suggested as a possible technique for model validation. By means of a topological analysis, we revisited this concept with the help o...

background. An intuitive description of the sudden transition of an autonomous optimizer with cognition into an “other-centered” mode of functioning is offered. This “bifurcation” is highly nontrivial. It presupposes a specific rewardability of the individual by the displayed joyfulness of the interaction partner. This is the case if the momentaril...

Abstract—The functional difference between human beings and animals is that human beings do normally become persons at a young age (about 1 ½ years old). So far, no animal has become a person. A recipe to change this was recently offered. Only if the new person is treated with the greatest affection can this experiment be ethically justified. Her h...

The temporal diagram of light rays going up and down between mirrors is the “WM diagram” presented in 1998 under the title "Gravitational slowing-down of clocks implies proportional size increase." Almost two decades later, the diagram could be completed to include not only time but also space. The crossing letter M-like and letter W-like zigzags o...

The theory of the famous Oppenheimer-Snyder paper of 1939 is re-told and put into perspective

The answer reads: “of course it can.” The experiment in question produces the hottest resident spot in the Universe down on earth. This fact, realized by the “LHC” experiment of CERN, is being withheld from the NSA by CERN. On the other hand, the appealing label used publicly by CERN – “pulling the Big Bang down onto earth” or more briefly “Big-Ban...

https://www.sjpub.org/sjp/sjp-287.pdf

The journal kindly invited me to offer a contribution after another clinical journal had solicited a paper on autism. Author was allowed to use the occasion to give more background information. This time around, author does not quote the grandmasters of the past like Rene Spitz and Mary Ainsworth but rather only describe the conditions under which...

http://www.ptep-online.com/index_files/2015/PP-43-09.PDF

contents freely available at http://www.hindawi.com/journals/tswj/si/845212/

Deterministic antidissipation is a new numerical observation made by using an advanced symplectic integration algorithm in long-term simulations of a Hamiltonian system . Two frictionless particles of unequal mass and kinetic energy were subjected to Newtonian-type interaction in a T-tube configuration; first under Newtonian repulsion , then under...

One of the editors of this book suggested including this true story about which I learned from my friend Konrad Zacharias Lorenz in 1966.

Forty years ago a causal therapy of autism was offered which has never been tried out by the therapeutic profession. It predictably is so effective that even members of other mirror-competent bonding species can be healed from their "physiological autism." Niklas Luhmann belonged to the therapy's supporters and Leo Szilard had anticipated it in fic...

The Einstein-Bell-Feingold experiment is reviewed and put into a 2 ½ millennia old context. There are only months to go until the experiment will be accomplished by ESA following 14 years of preparation. This “relativistic Bell experiment” is arguably the most important one of history. The riddle of the “assignment conditions” which complement the...

An informal attempt is made to convey the essence of a causal understanding of autism that was reached under the influence of my three great teachers, Konrad Lorenz, Gregory Bateson and Robert Rosen. Especially Gregory Bateson understood every detail. He was the father of the double-bind theory, an interactional trap that anyone can fall into as a...

https://link.springer.com/chapter/10.1007/978-3-319-64334-2_30 ------------------------------------------------------------------------------------------------------------------------------------- The basic laws of deterministic many-body systems are summarized in the footsteps of the deterministic approach pioneered by Yakov Sinai. Two fundamenta...

The book you hold in your hands is the outcome of the “2014 Interdisciplinary Symposium on Complex Systems” held in the historical city of Florence. The book consists of 37 chapters from 4 areas of Physical Modeling of Complex Systems, Evolutionary Computations, Complex Biological Systems and Complex Networks. All 4 parts contain contributions that...

http://eujournal.org/index.php/esj/article/view/4589/4360

Two building blocks valid in two unrelated physical disciplines, statistical mechanics and general relativity, respectively, have convergent implications for cosmology. Firstly, cryodynamics – the recent new sister discipline to thermodynamics which applies to gases that are made up from mutually attractive rather than repulsive particles – is anti...

The present list was compiled by a “specialist for non-specialization” who owes his scientific identity to the masters of three disciplines: physicist Carl-Friedrich von Weizsäcker, biologist Konrad Lorenz and mathematician Bob Rosen. With the in retrospect best findings compressed into a line or two, the synopsis brings hidden patterns to the fore...

You are around 50 years old in our story. Maybe it is a good idea to talk in this session and perhaps in two sessions about the connection between cosmology and your ideas?

In the previous session, we talked about evolution. Another subject with the potential for one or two sessions is symmetry. Let us talk about symmetry in nature, symmetry in mathematics and symmetry in physical laws. At first, let me ask you: How do you define symmetry? And secondly, what are your thoughts on symmetry in physical laws? Can you, ple...

We start the fourth session of recording the scientific autobiography. You now have received a conference folder which contained among others the Edward Lorenz paper of 1963. Next, I would like to learn how you proceeded in the chaos field, especially: how you created the chaos attractor, and how did your ideas and insights arise?

In the previous session we talked about endophysics. Now I want to continue with this topic by asking the question; what is Everett’s main idea, and what is the relation between your own idea of endophysics and that of Everett?

My first question: When did you first encounter the philosophy of science? When was that important point in your life?

In our new session we are going to talk about cryodynamics. Let me start with statistical mechanics. We have some postulates or axioms in thermodynamics, calling them “first law,” “second law,” “third law” and even “zeroth law.” Altogether we have four laws that we can call axioms, but some of them can apparently be derived from one of the others.

A new session. We again want to talk about cryodynamics, but this time on its applications. We talked about the theory in two previous sessions. My question is as follows; what is the application of cryodynamics to cosmology? What are the new results that we arrive at?

In this session I would like to come back to cryodynamics again. Let me ask you to explain it from the basis of the T-tube model, its structure and conception. In addition, I plan to ask you one question; I saw a paper outside physics of 2008 by Professor Zadeh, titled “Is there a need for fuzzy logic?” After more than 40 years of work he confronte...

In this session we want to consider the subject of human language. There are different viewpoints on the evolution of language held by philosophers, but I want to look at human languages from a dynamical-systems point of view. Before concentrating on language as a dynamical system, I would like to ask you; how do you look at the history and evoluti...

In today’s discussion I would like to address some fundamental questions. We have the famous list of the 23 Hilbert problems, some of which have been solved, some incompletely solved, some of which are still open problems, and some have been considered to be very vague. The “sixth Hilbert problem” was proposed belatedly at the end of the 1930s. Thi...

The concept of spin is important in quantum mechanics. Do you think quantum mechanics can present a complete explanation for it? Does this concept have a correspondence in classical physics as well? How do you explain it? In quantum mechanics, it is somehow explained with Planck’s constant. What is your explanation of the spin?

In this session I would like to ask a somewhat different question. It actually is motivated by Einstein. Can one expect a good influence of religion on the study of physics and its progress? Often one finds the opposite opinion among physicists—that as soon as we have progress in physics we do not need religion anymore. Some go as far as to say tha...

The brain equation is a solution to the “second survival problem.” The latter is called “positional adaptation.” It unlike Darwin’s first (“metabolic adaptation”) is history-independent. As such it is mathematically well posed. The equation applies to all life forms in the cosmos that live in a structured environment in which survival depends on po...

Let us try to explain how the universe evolved. After our talking about biological evolution, let me ask, can we speak of a Darwinian dynamics in cosmology?

Let us continue with the scientific biographical interview. Now you are between 45 and 50 years old. Let us start out with the meaning of infinity in mathematics and physics.What is the meaning of infinity in nature?

Let us discuss a new topic. In Chap. 9 we talked about cosmology and the Olemach theorem. Now I would like to propose a combined question; can one think about evolution from a dynamical-systems point of view?

Last time we talked about chaos and hyperchaos, while you were around 38, let us continue from this age.

In this session let us conclude the previous 24 sessions with the following question. You have worked and commented on a lot of topics in our previous interviews; do you consider the whole field to be rational, or are there some totally open things that need explanation, too? What is the meaning of rationalism in science?

In this session we decided to talk about some special names in physics. We could start with Newton, but let us start out with Einstein. People love to know more about him. I am sure you studied a lot regarding his life, his chapters and maybe his errors, if any. You can start from whatever point you wish. Maybe it is better if you mix both the scie...

In this session we will change the subject and come back to more fundamental questions in physics. The main subject I propose to talk about is the many body problem. As a first step, let me ask you; what is a two-body system? What are the special points? And if you like, we can then add a further body and discuss the phenomena characteristic of thr...

You are now 26 years old. Our last point was that you lost your position at Max Planck because your stipend had finished. Now, please, continue: What happened after that?

We enter the third session. You are now 35 years old and you just obtained a special folder from the United States that contained several papers on chaos, one of which was the Ed Lorenz paper

We talked on cosmology in Chap. 8 and I suggest we continue a little more. I would like to ask you, what are your ideas about the speed of light, about relativity theory, and what are your new contributions to these topics? Which insights do you consider important and what are the implications regarding cosmology?

There is a paper by Jim Yorke . He tried to find a mathematical model of the taffy pulling machines as a chaotic system. I am interested in your ideas concerning taffy as an example of chaos. Can we see hyperchaos in this example? And what is the importance of this physical model? Is it only a plaything or does it have consequences in chaos theory?

We already talked about the brain equation in detail, and we made the connection to dynamical systems and biology. It may be a good idea to talk about intelligences. What is human intelligence? And what about intelligence in animals? What does it mean if one animal is smarter than another? Can you make a link between the brain equation and this top...

Deterministic nonperiodic flow (of “chaotic” or “strange” or “tumbling” type, respectively) was first observed, in a 3-component differential system, by E. N. Lorenz in 1963. A 3-component abstract reaction system showing the same qualitative behavior is indicated. It consists of (1) an ordinary 2-variable chemical oscillator and (2) an ordinary si...

An open three-variable mass action kinetics is presented which exhibits chaotic behavior under numerical simulation. The elementary reactions of this system are at most of second order and satisfy the requirements of thermodynamics as long as the system is closed.

A macroscopic chemical oscillator involving 3 autocatalytic second-order reactions is simulated microscopically. A deterministic Newtonian simulation involving 1024 particles with a smooth 1/r potential in two dimensions is presented.

A form of the Verlet-algorithm for the integration of Newton's equations of motion is derived from Hamilton's principle in discretized space and time. It allows the computation of exactly time-reversible trajectories on a digital computer, offers the possibility of systematically investigating the effects of space discretization, and provides a cri...

A deterministic entropic measure is derived for the time evolution of Newtonian N-particle systems based on the volume of the instantaneously occupied phase space (IOPS). This measure is found as a natural extension of Boltzmann's entropy. The instantaneous arrangement of the particles is exploited in the form of spatial correlations. The new entro...

The usefulness of the Ott-Grebogi-Yorke control method is demonstrated by stabilizing a chaotic NMR-laser system around an unstable period-one orbit. We have used a six-dimensional delay-coordinate embedding technique in order to fully determine the stability properties of the orbit controlled. Our analysis yields small time-dependent perturbations...

A new synthesis based on microscopic classical thinking is attempted in the spirit of the molecular-dynamics-simulation (MDS) paradigm. Leibniz’s idea that joint scale transformations cancel out is invoked. Boltzmann discovered that a time reversal in the whole universe is undetectable from the inside. As a corollary, objective micro time reversals...

Both Fredkin's findings on the reversibility of logical operations and the novel capability to integrate Newton's equation of motion in an exactly reversible manner enables one to perform a gedankenexperiment in the form of a molecular dynamics simulation of the Universe. This leads to a new validation of the reversible structure of the Universe. A...

A piecewise-linear. 3-variable autonomous O.D.E. of C0 type, known to describe constantshape travelling waves in one-dimensional reaction-diffusion media of Rinzel-Keller type, is numerically shown to possess a chaotic attractor in state space. An analytical method proving the possibility of chaos is outlined and a set of parameters yielding Shilni...

By investigating the reaction diagram in its own right, it is possible to solve the problem of enumerating all the different types of mass action kinetics up to second order. The amount of non isomorphic complex sets for a given number of species and of non isomorphic reaction networks and reversible reaction networks which can be derived from a gi...

The complexity of dynamical behavior possible in nonlinear (for example, electronic) systems depends only on the number of state variables involved. Single-variable dissipative dynamical systems (like the single- transistor flip flop) can only possess point attractors. Two-variable systems (like an LC-oscillator) can possess a one-dimensional attra...

Poincaré half-maps can be used to characterize the behavior of recurrent dynamical systems. Their usefulness is demonstrated for a linear three-dimensional single-loop feedback system. In this example everything can be calculated analytically. The resulting half-maps are "benign" endomorphic maps with a complicated topological structure. This is su...

The separating mechanisms occuring in a class of Poincaré halfmaps that is induced by the flow of a saddle-focus are described quantitatively. The “critical spiral” is calculated explicitly inside the domain of the map. A complete hierarchy, consisting of three different types of separating mechanisms, is demonstrated. It is characterized in terms...

An example of a chemical reaction system producing a type of oscillation that is close to a quasi-periodic oscillation is presented. Such system may help clarify the relationship between quasi-periodicity and chaos.