Nonlinear Dynamical Systems: Book Suggestions

[verd]

Hi all,

I'm in a position where I have to teach myself an entire course in Dynamical Systems (mostly nonlinear, though there is a linear component)
I've got several books, including Strogatz (Nonlinear Dynamics and Chaos) and Bauer/Nohel's classic book (A Qualitative Theory of Ordinary Differential Equations).

I'm able to assimilate most of the theory I need from a combination of these books, without the need for detailed explanations from an instructor/TA.

Though, I'm having a lot of difficulty using the theory to solve problems. Each book provides problems at the end of the chapter, and I attempt to solve these problems, but I have no way of checking myself-- or to learn from my mistakes.

So I was wondering if anyone had a recommendation for a good Nonlinear Dynamics book that had a lot of problems and complete worked solutions. Something like one of those calculus study guides filled pretty much with problems and solutions...
(Something covering a bit of linear sys, nonlinear stability, lyapunouv functions... typical stuff)


Is anyone familiar with anything like this?


Many thanks.
-H

 

[jvicens]

i there!

First of all, kudos to you for taking on the challenge of teaching yourself an entire course in Dynamical Systems. It can be a daunting task, but with the right resources, it is definitely possible.

In terms of finding a book with a lot of problems and complete worked solutions, I would recommend "Differential Equations, Dynamical Systems, and an Introduction to Chaos" by Morris W. Hirsch, Stephen Smale, and Robert L. Devaney. This book covers a wide range of topics in dynamical systems, including linear systems, nonlinear stability, and Lyapunov functions. It also includes a large number of problems at the end of each chapter, with complete solutions provided in the back of the book.

Another helpful resource could be online problem sets and solutions from universities that offer courses in dynamical systems. Some universities, such as MIT, have openly available course materials that include problem sets and solutions for self-study.

Additionally, I would recommend seeking out online forums or communities where you can discuss and ask questions about specific problems with other individuals studying dynamical systems. This can provide valuable insight and help you learn from your mistakes.

Overall, the key to mastering problem-solving in dynamical systems is practice and persistence. Keep working through problems and seeking out resources, and you will see improvement over time. Good luck with your studies!