Looking for good intro books/texts on dynamical systems

In summary, the individual is taking a course in dynamical systems but is struggling to understand some of the concepts. They are looking for additional resources on the topic, preferably a book that provides a good introduction and includes examples and applications. They mention that they are not too concerned about proofs and are looking for something that is easy to understand. A suggested resource is the book Nonlinear Dynamics and Chaos by Strogatz, which is accessible and focuses on building understanding rather than proofs.
  • #1
chaose
10
0
I'm taking a course in dynamical systems and I'm struggling to grasp some of the concepts. The instructor only occasionally reference the textbook I'm using, which is
Differential Equations, Dynamical Systems, and An Introduction to Chaos 2nd Ed. (By Hirsch, Smale, and Devaney). I'm looking for addtional books/resources on this topic.

Ideally, I'm looking for something that serves as a good introduction to the subject of dynamical systems, so that I can easily understand the concepts. Addtionally, it would be nice after the concept explanation it would go into slightly more advanced applications. The more examples there are the better. Proofs are nice but I don't really care too much about them - it's more the application and east of understanding I care about.

any suggestions and ideas would be welcome.
 
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  • #2
shameless bump.
 
  • #3
Nonlinear Dynamics and Chaos by Strogatz is probably what you are looking for. I have only read a few sections here and there, but it is a really accessible and fun introduction to the topic. It is perhaps light on the proofs, but heavy on concepts and building understanding. The book assumes you know elementary differential equations, but not much more.

jason
 
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1. What is a dynamical system?

A dynamical system is a mathematical model that describes the behavior of a system over time. It consists of a set of equations that govern how the state of the system changes over time in response to its initial conditions and external influences.

2. Why are dynamical systems important?

Dynamical systems are important because they can be used to model and understand complex systems found in nature, such as weather patterns, population dynamics, and chemical reactions. They also play a crucial role in fields such as physics, biology, economics, and engineering.

3. What are some common examples of dynamical systems?

Some common examples of dynamical systems include the Lorenz system, which is used to model weather patterns, the Lotka-Volterra equations, which describe predator-prey interactions in ecology, and the logistic map, which shows how population growth can be affected by limited resources.

4. Are there any recommended introductory books or texts on dynamical systems?

Yes, there are several highly regarded books on dynamical systems for beginners, including "Nonlinear Dynamics and Chaos" by Steven Strogatz, "Dynamical Systems in Neuroscience" by Eugene Izhikevich, and "A First Course in Chaotic Dynamical Systems" by Robert Devaney. These books provide a solid foundation for understanding the key concepts and techniques in dynamical systems.

5. What background knowledge is required to study dynamical systems?

A basic understanding of calculus, linear algebra, and differential equations is recommended for studying dynamical systems. Some familiarity with computer programming and mathematical software such as MATLAB or Python can also be helpful in visualizing and analyzing dynamical systems.

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