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Questions related from Sajad Jafari
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...
29 April 2024 8,571 2 View
While most governments try to hide the facts and manipulate statistics about COVOD-19 due to political/economical/stupidity reasons, many physicians and scientists are currently working on finding...
04 March 2020 5,431 26 View
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...
12 February 2020 6,363 3 View
We have obtained MSF for a dynamical system. It is a line (while all MSFs I have seen are curves). Please see the attached picture. Is this a known phenomenon?
03 November 2019 7,621 0 View
We are working on some projects related to networks of coupled nonlinear oscillators. We want to obtain “Master Stability Function” (MSF) in our network. 1. Is there any sample code available in...
30 September 2018 9,550 3 View
Consider an autonomous dynamical system in the following form: x1' = f1(x1, x2, …, xn) x2' = f2(x1, x2, …, xn) ….. xn' = fn(x1, x2, …, xn) Suppose that X* is an equilibrium for this system. Is...
16 December 2016 7,940 15 View
Consider the time-series of one of the states (say x) in the Lorenz system. Also consider the time-series of one of the states (again say x) in the Rossler system. If we only have the signal of...
12 October 2016 5,999 6 View
Consider a 2D (or a higher dimension) chaotic map like Tinkerbell map: x(n+1) = x(n)2 -y(n)2 +a x(n) +b y(n) y(n+1) = 2x(n)y(n) +c x(n) +d y(n) Suppose that we don’t know the above equations and...
26 March 2016 7,797 3 View
It is claimed that human’s decision making is not logical necessarily [1]. Here is an example from [2]. Task 1: choose one of the following options: a) 80% chance to win 4000$. b) 3000$...
13 March 2016 2,779 9 View
I am aware of some examples of such cases but they are very rare. For example the attached figure shows period-doubling route to chaos based on the real data (for more details about this figure...
23 October 2015 9,828 14 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...
31 December 2014 7,829 9 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...
19 September 2013 5,658 9 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...
13 September 2013 9,052 19 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...
25 August 2013 1,903 13 View
I know there are many chaotic flows with fractal basin of attraction. Also 2D maps with fractal basin of attraction. Is there any piecewise continuous 1-D map with fractal basin of attraction? For...
23 June 2013 9,333 4 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' =...
17 June 2013 9,055 27 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...
16 May 2013 4,064 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?
10 May 2013 7,335 8 View
Sorry if I haven’t said my question well. Maybe the following example helps. Consider a chaotic system (flow, not map) which is described by x1' = f1(x1, x2, ... , xn) x2' = f2(x1, x2, ... ,...
03 May 2013 8,806 2 View
I know there is one system in [1], but I haven’t seen any other case. [1] Wang, X. & Chen, G. [2012] “A chaotic system with only one stable equilibrium,” Commun. Nonlinear Sci. Numer. Simulat....
03 May 2013 9,160 2 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...
02 May 2013 4,539 14 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...
29 April 2013 1,967 2 View
How can we investigate the stability of a specific equilibrium in a 3-D flow when the real part of one (or more) of the eigenvalues is zero? I think such systems are called nonhyperbolic. I know...
27 April 2013 9,036 3 View
