It is known that in order to quantify chaos in a dynamic system, the maximum Lyapunov exponent must be detected, but before applying Lyapunov detection, is there any way to know at a glance a dynamic system is chaotic ?
Is it enough to see that the phase space is fully and disorderly filled up? It happens that in a dynamic system I am computer simulating I get a fully and completely disordered state space. I want to know if this is an indication of chaotic behavior.
Thanks in advance to those who answer !!!
Dear Javier Montenegro Joo
These articles will guide you on the right track, have a look:
1. https://www.sciencedirect.com/science/article/pii/S2666389921000404
2. https://www.mdpi.com/2076-3417/11/1/437/pdf
3. https://www.nature.com/articles/s41467-019-10040-3
Kind Regards
Qamar Ul Islam
Dear Javier Montenegro Joo,
A simple and crude way that a system is said to be chaotic if it shows a sensitive dependence on the choice of the initial conditions, however there are more elaborate and rigorous methods which can indicate this characteristic. For that i suggest you to see links on topic.
https://uh.edu/nsm/news-events/stories/2019/0116-dynamical-systems.php
https://www.osti.gov/etdeweb/servlets/purl/20109628
https://www.whoi.edu/fileserver.do?id=21476&pt=10&p=17353
https://play.google.com/store/books/details/Non_traditional_Dynamics_in_Electronics_Theory_and?id=3qbvBQAAQBAJ&hl=en_US&gl=US
https://www.taylorfrancis.com/books/edit/10.4324/9780203866160/managing-complex-governance-systems-geert-teisman-arwin-van-buuren-lasse-gerrits
https://www.springer.com/gp/book/9783034875202
Chapter Chaotic Dynamics and Complexity in Real and Physical Systems
Article Chaotic Behavior in a Switched Dynamical System
Best regards
simple way that a system is said to be chaotic is if it shows a sensitive dependence on the choice of the initial conditions.
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