I How to check chaotic system using Lyapunov

24
1
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)

upload_2018-12-15_20-13-22.png


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

Thanks, your consideration is appreciated!
 

Attachments

jim mcnamara

Mentor
3,555
1,778
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.
 
24
1
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
1,216
158
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).
 

Want to reply to this thread?

"How to check chaotic system using Lyapunov" You must log in or register to reply here.

Related Threads for: How to check chaotic system using Lyapunov

  • Posted
Replies
2
Views
2K
Replies
1
Views
772
Replies
16
Views
995
Replies
1
Views
792
Replies
8
Views
4K
  • Posted
Replies
17
Views
2K
Replies
5
Views
576
  • Posted
Replies
2
Views
1K

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

Hot Threads

Top