Nonlinear Systems

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2 Why synchronization in chaos?
By Suresh mrp · Vel Tech - Technical University

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12 What is dynamic stability definition in human movement? We say a state is stable, what is dynamic stability?
By Reza Saber · Amirkabir University of Technology

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9 Does a 3-D chaotic system (flow) with only a curve equilibria or with only a surface equilibria exist? Is that possible?
By Sajad Jafari · Amirkabir University of Technology

John Pearson · Los Alamos National Laboratory

Sajad, that is interesting. I didn't think of that (obviously)!

Sajad, that is interesting. I didn't think of that (obviously)!

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Open How can we treat the matrix B in X'=Ax+Bu when the forcing function that produce B is a step function in design of controller for the system?
If the system arose from linearization process, matrix B will contain t terms. Does this suggest a variable B? If yes, a literature on approach to tre... [more]

If the system arose from linearization process, matrix B will contain t terms. Does this suggest a variable B? If yes, a literature on approach to treat this case will be appreciated.

By Kamil Abdulrahman · Universiti Teknologi Malaysia

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2 Does anyone know some conservative chaotic systems (3-D flows)?
By Sajad Jafari · Amirkabir University of Technology

Elena Kartashova · Johannes Kepler Universität Linz

A lot of examples of chaotic conservative systems are given in my book "Nonlinear Resonance Analysis" (Cambridge University Press, 2010). For instance... [more]

A lot of examples of chaotic conservative systems are given in my book "Nonlinear Resonance Analysis" (Cambridge University Press, 2010). For instance, a resonance cluster in a 3-wave which consists of two connceted triads (see figure 4.6, p.111 in the book).

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13 Can a strange attractor have a 2-D projection in the form of limit cycle?
By Sajad Jafari · Amirkabir University of Technology

P. Allen · Cranfield University

A 2-D projection of a chaotic system is always possible but the motion would not be unidorectional around the limit cycle. There would be reversals an... [more]

A 2-D projection of a chaotic system is always possible but the motion would not be unidorectional around the limit cycle. There would be reversals and accellerations as the behaviour followed its path on the multi-dimensional chaotic attractor.

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3 State space reconstruction: How can we reconstruct the state space of scalar time series?
By Reza Saber · Amirkabir University of Technology

Aggelos Iliopoulos · Democritus University of Thrace

You can use the Ruelle's formula which provides an upper bound for the estimation of D2: D2 <= 2log10 (N) where N is the time series length. In genera... [more]

You can use the Ruelle's formula which provides an upper bound for the estimation of D2: D2 <= 2log10 (N) where N is the time series length. In general, you need long time series in order to estimate D2 in high embedding dimensions

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13 How to fit two-three sum of exponential decay nonlinear model?
By Dushyant Kumar · Cornell University

Herbert Homeier · Universität Regensburg

As far as I understand, the fit of a sum of exponentials to measured data is an old and quite tricky problem. There is for instance a section titled "... [more]

As far as I understand, the fit of a sum of exponentials to measured data is an old and quite tricky problem. There is for instance a section titled "Separation of exponentials" in the classic book of Lanczos "Applied Analysis" (Chap. IV, §23). Some of the relevant input has already been mentioned. The number of nonlinear parameters should be kept rather low ("with three exponentials you can fit an elephant" ;)), due to the nonlinearity of the functional to be minimized there may be several solutions that describe the data equally well for a given set of data, and the requirements on the data as regards accuracy and number and distribution of data points may be rather high. Older functionals to be used as target functions are simply least-squares, where the tricky part may be the distribution of points and weights. There are other methods like maximum entropy that are used to regularize the inherent problems of such inverse problems by probabilistic means, e.g. in image restauration.

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1 Data fitting and parameter estimation in Nonlinear Differential Equations, like in SIR model using MATLAB with DATA constrainsts..
By Harsh Kushwah · The LNM Institute of Information Technology

Sanjay Lamba · The Central University of Rajasthan

Dear Harsh I suggest you some following reference for deal with this problem 1. Simple mathematical models with very complicated dynamics by May 2.Fo... [more]

Dear Harsh I suggest you some following reference for deal with this problem 1. Simple mathematical models with very complicated dynamics by May 2.Formulating variable carrying capacity by exploring a resource dynamics-based feedback mechanism underlying the population growth models by Hsin-i Wua, Amit Chakraborty , Bai-Lian Li , Charles M. Kenerley

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2 What sense have derived fractional to control theory?
By Jessica Mendiola · Instituto Potosino de Investigación Científica y Tecnológica

Yuri Dimitrov · The Ohio State University

Hi Jessica, Maybe try to find some meaning of the Caputo derivative at the initial point: aDa[f(a)] from the Mean-Value Theorem ( like Proposition 2... [more]

Hi Jessica, Maybe try to find some meaning of the Caputo derivative at the initial point: aDa[f(a)] from the Mean-Value Theorem ( like Proposition 2.2 in Fractional Taylor Series for Caputo Fractional Derivatives. Construction of Numerical Schemes by David Usero). If we let x->a in the mean value theorem we obtain a similar formula to the definition of classical derivatives. Another place to try is Geometric and Physical Interpretation of Fractional Integration and Fractional Diﬀerentiation by Igor Podlubny.

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3 How can I make Backstepping Control Design?
By Abdelaziz Mansour · The American University in Cairo

Abdelaziz Mansour · The American University in Cairo

Can you send the e-mail of your colleague again

Can you send the e-mail of your colleague again

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6 How can I convert a model to a matrix?
By Zohreh Jafari · University of Isfahan

Zohreh Jafari · University of Isfahan

Thank you dear Ernesto and dear Rodrigo. your comments were helpful.

Thank you dear Ernesto and dear Rodrigo. your comments were helpful.

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1 Can anyone direct me on the most appropriate software/program to analyse bubble train in microfludics?
By Zuonaki Ongodiebi · The University of Manchester

Lingxue Kong · Deakin University

You could try some image processing software which could provide you with all sorts of information. You could develop your own software using Matlab e... [more]

You could try some image processing software which could provide you with all sorts of information. You could develop your own software using Matlab etc.

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2 Modelling a time series
By Samuel Ogunjo · Federal University of Technology, Akure

Samuel Ogunjo · Federal University of Technology, Akure

Thanks. Most of the published algorithms are like a foreign language. Can you help me with an algorithm preferably in matlab or fortran. Thanks

Thanks. Most of the published algorithms are like a foreign language. Can you help me with an algorithm preferably in matlab or fortran. Thanks

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2 How does one implement wetting and drying? Is it just by ensuring positive height or by incorporating some terms in the model equations?
By Chinedu Nwaigwe · The University of Warwick

Chinedu Nwaigwe · The University of Warwick

How then can one implement that. I want to learn from first principle. But the papers I have are not presenting the fundamental steps. Please, kindly ... [more]

How then can one implement that. I want to learn from first principle. But the papers I have are not presenting the fundamental steps. Please, kindly help me with some starting materials.

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5 I have a nonlinear system. Please help me out in computing a monodromy matrix.
By Mala Champaka · Manipal Institute of Technology

Nils Wagner · Intes GmbH Stuttgart

Hi, I am only interested in linear systems so far. The monodromy matrix \Phi can be calculated numerically by repeated integration of the systems equ... [more]

Hi, I am only interested in linear systems so far. The monodromy matrix \Phi can be calculated numerically by repeated integration of the systems equations \dot{y} = A(t) y over one period T, starting from independent sets of initial conditions. It is convenient to use the columns of the identity matrix I_m as initial vectors to start from. y_i(0) = e_i, where e_i denotes the i-th column of the identity matrix \Phi = [y_1(T),\dots, y_m(T)] The complex eigenvalues \lambda \Phi x = \lambda x of the monodromy matrix are calculated numerically and max( | \lambda_i |) determines the stability. How about eigenvalues |\lambda_i| = 1 \pm \epsilon \epsilon << 1 ? It might be difficult to judge the stability. What integrators (Runge-Kutta, Newmark, etc.) are recommended ? What eigensolver should be used to compute the eigenvalues ?

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1 Discontinuous system in economic models.
By Douglas Duarte Novaes · Universidade Estadual de Campinas

Aragorn Napoleon · Peking University

Disequilibrium growth theory : an application of the Filippov solution to economics Author:Marrewijk, Charles van. Publish:Avebury,

Disequilibrium growth theory : an application of the Filippov solution to economics Author:Marrewijk, Charles van. Publish:Avebury,

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1 Why is it difficult to prove global stability in epidemic models like SIR, SEIR etc as compared to prey predator models?
By Archana Bhadauria · University of Lucknow

José Luis Bravo Trinidad · Universidad de Extremadura

Global stability is difficult even in predator-prey models. But in epidemic models you are in a higher dimension space (you have more equations) and t... [more]

Global stability is difficult even in predator-prey models. But in epidemic models you are in a higher dimension space (you have more equations) and then the dynamics can be more complicated.

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7 contacts
By Paul Krot · National Academy of Sciences of Ukraine

Douglas Duarte Novaes · Universidade Estadual de Campinas

Hello. I work with piecewise continuous systems. Recently, I have extended, for discontinuous systems, the well known "Averaging Theorem" to find pe... [more]

Hello. I work with piecewise continuous systems. Recently, I have extended, for discontinuous systems, the well known "Averaging Theorem" to find periodic solutions. Currently, I am working with decompositions of piecewise continuous vector fields; and with a version of 16 Hilbert's problem for discontinuous systems which deals with limit cycles of polynomials vector field on the plane.

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3 Multi-resonace response of nonlinear oscillators
By Semiu Kareem · Redeemer's University

Muhammad Ayub · Quaid-i-Azam University

Dear Kareem the "Regular and Chaotic Dynamics" by Lichtenberg and Lieberman has a status of bible in nonlinear dynamics but for beginners it is very d... [more]

Dear Kareem the "Regular and Chaotic Dynamics" by Lichtenberg and Lieberman has a status of bible in nonlinear dynamics but for beginners it is very difficult to understand it. Another book which is simple to follow and understand you may consult as well. The title of the book is "Physics of Chaos in Hamiltonian Systems" by George M. Zaslavsky.

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Open Complimentary subscription of “International Journal of Mathematics and Computation”
Complimentary subscription of “International Journal of Mathematics and Computation” Invited to join: http://www.researchgate.net/group/Intern... [more]

Complimentary subscription of “International Journal of Mathematics and Computation” Invited to join: http://www.researchgate.net/group/International_Journal_of_Mathematics_and_Computation/ International Journal of Mathematics and Computation ISSN 0974-570X (Online), ISSN 0974-5718 (Print) www.ceser.in/ijmc.html Dear Colleagues, Following issues are available without subscription fee. Just REGISTER your-self to download the paper(s) form above special volume http://www.ceser.in/ceserp/index.php/ijmc/user/register 2011, Volume 11, Number J11 (Special Volume) Second Special Volume on The 6th International Conference: Dynamical Systems and Applications-2010, Antalya–Turkey, July 10-14, 2010 2011, Volume 10, Number M11 (Special Volume) First Special Volume on The 6th International Conference: Dynamical Systems and Applications-2010, Antalya–Turkey, July 10-14, 2010 With Regards, Haydar Akca Editors-in-Chief International Journal of Mathematics and Computation www.ceser.in/ijmc.html www.ceserp.com www.ceserpublications.com www.ceser.in/ijmc.html

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Open nonlinear QM
When science try to study nonlinear quantum mechanics, begins introducing nonlinear terms in QM. It is like non-linearizing the linear QM. Can QM be c... [more]

When science try to study nonlinear quantum mechanics, begins introducing nonlinear terms in QM. It is like non-linearizing the linear QM. Can QM be complete if it uses NLS equation from the beginning?. The blowing up of the wavefunction could imply some new definitions in QM?

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