I have a problem involving the new chaotic system dubbed as the Chen System. This involves a system of coupled nonlinear ordinary differential equations. My problem is to determine for which parameters a, b, and c would yield a periodic and chaotic solution. Here is the Chen System

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I am given the initial condition (t=0) that a particle lies on the xyz-plane at a point (-10,0,35). I was notified that if I plugged in a=40, b=5, and c=30, the trajectory of the particle will be chaotic. On the other hand, if I retained the values of a and c, and changing b to b = 10, periodic solutions will be obtained. My concern relies on how were these values picked. Is there any sort of mathematics (analytically) that was used here? I would appreciate any help that you would render. Below is the graph for the chaotic path of the particle.

enter image description here

  • $\begingroup$ Welcome to Physics SE! First, let me comment on the format: The equations become much easier to read, search and edit when mathjax is used. It'd be great if you could use it in your next posts (or even improve this one already). Talking about equations, are you aware that your system is remarkably similar to the Lorenz equations? Do you have a reference for this "Chen System"? Regarding your questions, yes, there are analytical methods, but we often have to resort to numerical ones. $\endgroup$
    – stafusa
    Jan 8 at 12:35
  • $\begingroup$ @stafusa Thank you so much for the warm welcome! I am aware that this system is Lorenz-like but my question relies on the analytical methods and concepts within it. I tried to read articles involving it but, it turns out that I cannot even comprehend it. Here is a sample reference paper involving the Chen System: researchgate.net/publication/… $\endgroup$ Jan 9 at 1:41
  • $\begingroup$ Lawrence, since this is established theory, papers tend to be very concise and it's better to resort to books. Some recommendations can be found here: Self-study book for dynamical systems theory?. $\endgroup$
    – stafusa
    Jan 9 at 2:13

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