I How to check chaotic system using Lyapunov

ohaited

Greetings!

Hey, can anyone help me? I need an explanation how can Lyapunov help me to check the system weather it is chaotic or not. Let say I have this equation Rossler System Eq.(1)

So how can you tell that the system have chaotic behavior or not? Does it depends on parameters? or from initial constant (a,b,c)?

A general and specific clarification is needed. Because I have this paper research that talk about Rossler System Eq. (1) can have chaotic behavior when the initial a=b=0.2 and c= 5.7

Attachments

• 4.4 KB Views: 298
Related Differential Equations News on Phys.org

jim mcnamara

Mentor
Could you please tell us the title of the paper and where/when it was published? It might help a lot to give you the best answer.

ohaited

Could you please tell us the title of the paper and where/when it was published? It might help a lot to give you the best answer.

Hey there, sorry for not attaching the paper with my question. So here it is: Paper

Filip Larsen

Gold Member
So how can you tell that the system have chaotic behavior or not? Does it depends on parameters? or from initial constant (a,b,c)?
In short you can determine if a particular system is chaotic by solving the differential equations numerically and calculate the Lyapunov exponents along the (non-transient) trajectory. If there is at least one positive Lyapunov exponent then the trajectory is chaotic and hence the system for its given parameters and initial state is considered chaotic.

For a practical guide on how to calculate it you may be inspired by the description on http://sprott.physics.wisc.edu/chaos/lyapexp.htm. Way back at university I used Practical Numerical Algorithms for Chaotic Systems by Parker and Chua, but that is a bit old now (but most likely still relevant).

"How to check chaotic system using Lyapunov"

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving