I need sources to learn about dynamic systems

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Discussion Overview

The discussion revolves around finding resources to learn about dynamic systems, chaotic systems, and their characteristics. The focus includes theoretical understanding, special points in dynamic planes, and the relationship between dynamic chaos and concepts like the butterfly effect. Participants also touch on specific questions related to stability and types of systems.

Discussion Character

  • Exploratory
  • Homework-related

Main Points Raised

  • The original poster seeks sources to understand dynamic systems and chaotic systems, specifically regarding characteristics and stability of special points.
  • Questions posed include the relationship between dynamic chaos and the butterfly effect, the basis of population dynamic models, and characteristics of chaotic dynamic system attractors.
  • The original poster expresses uncertainty about identifying special points in a dynamic system plane, suggesting a possible homoclinic bifurcation.
  • Some participants recommend the classic text by Strogatz as a foundational resource.
  • Participants also mention Strogatz's lectures as additional learning materials.

Areas of Agreement / Disagreement

Participants generally agree on the value of Strogatz's work as a resource, but the discussion remains unresolved regarding the specific questions raised by the original poster.

Contextual Notes

There is a lack of consensus on the identification of special points in the dynamic system plane, and the original poster's questions highlight potential gaps in their current literature and understanding.

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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