How to identify if a system exhibits chaos?

[Tahmeed]

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

 

[jedishrfu]

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.

 

[Khashishi]

One way is to use the Lyapunov exponent as a quantitative measurement of the chaos.