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Questions related from Sajad Jafari
We are working on some projects about dynamical analysis of two dimensional oscillators described by differential equations. We appreciate if you can introduce us the interesting cases you have...
08 August 2017 976 10 View
There are some evidences about the existence of chaotic patterns in our body [1-4]. However I am surprised why such examples are very rare and barely investigated. Especially I am interested to...
11 November 2016 2,280 3 View
I am working in department of biomedical engineering, Amirkabir University of Technology, Tehran, Iran. In our department people are working in different groups (biomaterial engineering,...
07 July 2016 5,199 2 View
“Large-scale signatures of unconsciousness are consistent with a departure from critical dynamics” http://rsif.royalsocietypublishing.org/content/13/114/20151027 Based on the above recent study,...
05 May 2016 6,396 3 View
Most familiar examples of low-dimensional chaotic flows occur in systems having one or more saddle points. Such saddle points allow homoclinic and heteroclinic orbits and the prospect of...
10 October 2015 6,204 1 View
When we want to plot a bifurcation diagram for a flow or map, we should consider some important points. Some of them have been mentioned in [1]. For example we should be careful about coexisting...
12 December 2014 854 11 View
Most of the continuous chaotic systems (chaotic flows) like Lorenz, Rössler, Sprott systems (cases B-S) have a Kaplan–Yorke dimension slightly greater than 2:1. Is there any 3D dissipative chaotic...
12 December 2014 679 6 View
I have asked a similar question before. I thank those participated and helped; however I didn’t find my answer. Consider the system described in the following ODEs:dx/dt = 1 +z^2 -w^2 -0.01xdy/dt...
11 November 2014 8,136 13 View
I mean chaotic flows. That is possible for chaotic maps.
04 April 2014 8,382 11 View
If I am not wrong, if such systems exist, they are examples of non-Shilnikov chaos. I will mention systems with no equilibrium [1] or with only stable equilibria [2] as other examples of...
04 April 2014 2,226 5 View
I am dealing with some 3-D flows which I suspect are chaotic. Can someone investigate the following three systems and tell me if they are really chaotic (and bounded, not chaotic in transient and...
09 September 2013 9,482 21 View
Consider a general 2D system: x' = f(x,y) y’ = g(x,y) Do you know any such system (preferably a simple one, ideally quadratic) which has more than one limit cycle? I would prefer it if there was...
09 September 2013 3,920 10 View
Consider a general 2D system: x' = f(x,y) y’ = g(x,y) Do you know any such system which has a limit cycle while there is no equilibrium in it? For example the famous Van Der Pol is not an answer;...
08 August 2013 4,803 6 View
Consider the famous Lorenz system: x' = 10(y-x) y’ = x(R-z)-y z’ = xy-8/3*z What is in there when R = 28, which is not in there when R = 26? I want an answer which will not be related to...
08 August 2013 7,098 14 View
Consider a general 3D system like: x' = f1(x,y,z) y' = f2(x,y,z) z' = f3(x,y,z) Can we predefine f1, f2 and f3 in such a way that if there is any strange attractor, it will have some certain...
08 August 2013 2,919 7 View
Recently there has been increasing interest in finding and studying rare examples of simple chaotic systems such as those in which there are no equilibria or in which any existing equilibria are...
08 August 2013 2,839 11 View
In genetic science, it is well known that a specific genetic behavior is influenced by one or several other genes. There is a similar subject in Genetic Algorithm (GA), called Epistasis, which is...
08 August 2013 3,885 3 View
We know that some apparently "4-D systems" are just 3-D systems "lifted" into a higher dimension. For example, take the simplest chaotic jerk system: x' = y y' = z z' = -az + y^2 – x Let w = z' =...
06 June 2013 8,825 28 View
Consider the famous Van Der Pol system: x' = y y’ = ay(1-x^2)-x Where a is for example 2. Is there any way to find its limit cycle (attached picture) based on the equations and not simulating...
06 June 2013 2,616 30 View
Consider a system with 2 states, M and L, with the following ODEs: dM/dt = 1 +L^2 -0.01M dL/dt = -1 +M^2 -0.01L It is certainly a dissipative system. I know if we use complex variables for M...
06 June 2013 7,639 34 View
We know that famous Lorenz system firstly developed as a model for atmospheric convection. Is there any real data which can show that model is acceptable? There are 3 parameters in Lorenz...
06 June 2013 4,450 36 View
Consider a chaotic system (flow, not map) which is described by: x1' = f1(x1, x2, xn) x2' = f2(x1, x2, xn) ….. xn' = fn(x1, x2, xn) Suppose that we project the strange attractor of this system...
05 May 2013 1,203 15 View
I mean a 3D chaotic continuous system in which any point on a specific curve (or a surface) is equilibrium and no other equilibrium exists beside that. Any idea about characteristics of such systems?
05 May 2013 6,644 9 View
I have some 3D conservative systems. They have positive largest Lyapunov exponent. It means they are chaotic. However there can be some problems: 1. Numerical errors in calculating Lyapunov...
05 May 2013 2,771 17 View
I know Sprott-A (Nose-Hoover system), and a system Heidel and Zhang investigated in “Nonchaotic and chaotic Behavior in Three-Dimensional Quadratic Systems: Five-One Conservative Cases” (which I...
04 April 2013 201 3 View
We are working on a chaotic map. The map completely continues and differentiable map with the following structure: X_n+1 = f(X_n,Y_n) Y_n+1 = g(X_n,Y_n) When we plot the bifurcation diagram,...
04 April 2013 1,518 11 View
In many science fiction movies (e.g. Matrix, Wanted, Spiderman, and Shinobi) there are scenes in which for superheroes time passes slower. Lots of times, what they do is similar to what their...
04 April 2013 3,518 14 View
