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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FAQ: I need sources to learn about dynamic systems

What are some recommended textbooks for learning about dynamic systems?

Some highly recommended textbooks for learning about dynamic systems include "Dynamic Systems: Modeling, Simulation, and Control" by Craig A. Kluever, "Feedback Control of Dynamic Systems" by Gene F. Franklin, J. Da Powell, and Abbas Emami-Naeini, and "Nonlinear Dynamics and Chaos" by Steven H. Strogatz. These books cover a range of topics from fundamental principles to advanced concepts in dynamic systems.

Are there any online courses that focus on dynamic systems?

Yes, there are several online courses available. Websites like Coursera, edX, and MIT OpenCourseWare offer courses on dynamic systems. For example, "Control of Mobile Robots" on Coursera, "Introduction to Control System Design" on edX, and "Dynamics and Control I" on MIT OpenCourseWare are excellent starting points.

What are some useful software tools for simulating dynamic systems?

MATLAB and Simulink are widely used for simulating dynamic systems due to their robust toolsets and extensive documentation. Other useful software includes Mathematica, which is great for symbolic computation and dynamic system analysis, and Python with libraries such as SciPy and NumPy for more customizable simulations.

Where can I find research papers and articles on dynamic systems?

Research papers and articles on dynamic systems can be found in academic journals such as the "Journal of Dynamic Systems, Measurement, and Control" and the "IEEE Transactions on Automatic Control." Websites like Google Scholar, ResearchGate, and JSTOR also provide access to a wide range of research papers in this field.

What are some key concepts I should understand when studying dynamic systems?

Some key concepts to understand when studying dynamic systems include state-space representation, stability analysis, feedback control systems, linear and nonlinear dynamics, and time-domain and frequency-domain analysis. A solid grasp of differential equations and linear algebra is also essential for understanding and modeling dynamic systems.

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