I need sources to learn about dynamic systems

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SUMMARY

The discussion focuses on learning resources for dynamic systems and chaotic systems, particularly for an upcoming exam. Key topics include the characteristics of dynamic systems, special points in the dynamic plane, and the relationship between dynamic chaos and the butterfly effect. Participants recommend starting with Steven Strogatz's classic text and his lecture series for foundational knowledge. The discussion also highlights the importance of understanding stability in special points like saddles, spirals, and centers.

PREREQUISITES
  • Understanding of dynamic systems theory
  • Familiarity with chaotic systems and their characteristics
  • Knowledge of stability analysis in dynamical systems
  • Basic concepts of bifurcation theory
NEXT STEPS
  • Study Steven Strogatz's book "Nonlinear Dynamics and Chaos"
  • Watch Strogatz's lecture series on dynamic systems
  • Research the butterfly effect in chaotic systems
  • Explore population dynamics models and their applications
USEFUL FOR

Students preparing for exams in dynamic systems, researchers in chaos theory, and anyone interested in the mathematical modeling of complex systems.

Ugnius
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Hi! I have exam in couple of weeks , and now am looking for sources to learn about dynamic systems , chaotic systems and etc.
My main goal is to learn characteristics of such systems , learn about special points in dynamic plane.
For the most part we used to create dynamic system simulations like finding special points like saddles , spirals and centres , indentifying their stability. Now i'll need to do that in theory exam. I'll post some questions to give you better representation.
Examples:
How is dynamic chaos related to butterfly effect?
What are population dynamic models based on?
What are characteristics of chaotic dynamic system attractors?
On the picture below , you see a dynamic system plane.
1684438616917.png

Is this system conservative or dissipative ? Is this system linear?
What special points do you see here , are they stable?
( On this last question , i'm especially lost , i've been looking to the literature given , but could find nothing similar , for me it looks like this is homoclinic bifirculation , but im not sure )

I don't want to make this post any longer, i'm very thankful in advance for anyone willing to guide me in a right way. Any source of information like books , threads or youtube videos will be helpful.
 
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The classic text here is by Strogatz
 
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Here are some Strogratz lectures
 
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Muu9 said:
The classic text here is by Strogatz
Yup always start with that one
 
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malawi_glenn said:
Yup always start with that one
Frabjous said:
Here are some Strogratz lectures

Muu9 said:
The classic text here is by Strogatz
Thank you!
 
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