I need sources to learn about dynamic systems

In summary, the conversation is about someone preparing for an exam on dynamic systems and looking for sources to learn about chaotic systems and their characteristics. They have previously created dynamic system simulations and now need to apply their knowledge in a theoretical exam. They ask about the relationship between dynamic chaos and the butterfly effect, the basis of population dynamic models, and the characteristics of chaotic dynamic system attractors. They also ask about the properties of a specific dynamic system shown in a picture. The conversation ends with a request for sources of information, particularly mentioning the lectures and text by Strogatz.
  • #1
Ugnius
54
10
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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  • #2
The classic text here is by Strogatz
 
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  • #3
Here are some Strogratz lectures
 
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  • #4
Muu9 said:
The classic text here is by Strogatz
Yup always start with that one
 
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  • #5
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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1. What are dynamic systems?

Dynamic systems refer to a class of systems that change or evolve over time. These systems can be found in various fields such as physics, biology, economics, and engineering.

2. Why is it important to learn about dynamic systems?

Studying dynamic systems allows us to understand complex phenomena and how they change over time. This knowledge can be applied to various real-world problems, such as predicting weather patterns, analyzing stock market trends, and designing efficient systems.

3. What are some common examples of dynamic systems?

Some common examples of dynamic systems include the motion of planets in our solar system, the growth of populations in biology, and the behavior of economic markets. Other examples can include chemical reactions, weather patterns, and traffic flow.

4. How can I learn more about dynamic systems?

There are various resources available to learn about dynamic systems, such as textbooks, online courses, and research papers. It is recommended to start with a basic understanding of mathematics and physics, as these are fundamental to studying dynamic systems.

5. What are some key concepts to understand in dynamic systems?

Some key concepts in dynamic systems include stability, equilibrium, feedback loops, and nonlinear dynamics. It is also important to understand how different variables and parameters can affect the behavior of a system over time.

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