I How to identify if a system exhibits chaos?

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To determine if a nonlinear equation exhibits chaos, one key indicator is that the system's orbits do not return to the same point and are aperiodic. Chaos is characterized by unpredictable values over time, making long-term predictions impossible. Other behaviors in nonlinear systems include multistability, where multiple stable states exist, and amplitude death, where oscillations cease due to interactions within the system. The Lyapunov exponent can be used as a quantitative measure to assess chaos. Understanding these concepts is essential for analyzing nonlinear dynamic behaviors effectively.
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How to tell if a non linear equation exhibits chaos?
Sorry, I am a beginner on this topic. And my library doesn't have book on this topic. I only read about this from John R Taylor's Mechanics book. I am looking for further resources.
TIA
 
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One clue is that the system orbits don't return to the same spot or are aperiodic.



https://en.wikipedia.org/wiki/Nonlinear_system

Types of nonlinear dynamic behaviors
  • Chaos – values of a system cannot be predicted indefinitely far into the future, and fluctuations are aperiodic.
  • Multistability – the presence of two or more stable states.
  • Amplitude death – any oscillations present in the system cease due to some kind of interaction with other system or feedback by the same system.
  • Solitons – self-reinforcing solitary waves.
 
One way is to use the Lyapunov exponent as a quantitative measurement of the chaos.
 
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