Sajad Jafari

20 Questions 40 Answers 0 Followers

Questions related from Sajad Jafari

Which unsolved problem or question you have in mind about chaos and chaotic systems?

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 8,372 2 View

How we engineers and mathematicians can be of help in fighting COVOD-19?

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 5,335 26 View

What is the importance of transient stages in obtaining fractal topologies?

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 6,297 3 View

Line-Shape Master Stability Function (MSF): Is it ordinary?

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 7,567 0 View

Can anybody help us with obtaining a code to calculate “Master Stability Function”?

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 9,483 3 View

Is that possible to have a dynamical system with an equilibrium in which all eigenvalues are zero?

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 7,886 15 View

Can we separate two chaotic signals when they are mixed? Especially when there is no information about their sources (blind signal separation)?

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 5,933 6 View

Is that possible to calculate Largest Lyapunov Exponent in a 2D chaotic map, without its equations, having only time series of one state?

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 7,728 3 View

Is there any period-doubling route to chaos in REAL biological systems proved by real experiments?

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 9,764 14 View

Which important points should be considered in plotting a bifurcation diagram?

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 7,771 9 View

Is there any 2D system (flow) with more than one limit cycle?

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 5,592 9 View

Which one of the following systems is a bounded chaotic system?

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 8,983 19 View

What is the cause of chaos in a dynamical system?

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 1,802 13 View

Is there any piecewise continuous 1-D chaotic map with fractal basin of attraction?

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 9,259 4 View

How can we say for sure that a 4-D ODE is really 4-D and cannot be reduced to 3-D?

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 8,977 27 View

What is the best method to investigate the existence of chaos in a 3D conservative continues system (flow)?

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 4,000 15 View

Does a 3-D chaotic system (flow) with only a curve equilibria or with only a surface equilibria exist? Is that possible?

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 7,271 8 View

Is there any chaotic system in which if one state be zero, the velocity of that state is zero?

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 8,728 2 View

Can a strange attractor have a 2-D projection in the form of limit cycle?

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 4,485 14 View

Does anyone know some conservative chaotic systems (3-D flows)?

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 1,917 2 View