Easy study material to define the normal form of a differential system

[marellasunny]

Could someone suggest me an easy guide to transforming a system of differential equations into normal form around a particular point?

As I understand, normal forms are used in border collision bifurcations to define the new set of coordinates around the parameter value $\mu _0$. By doing this, we accomplish finding the trajectory of the solution curve in the new half of the plane, am I right? (assuming our state space is divided into 2 halves)

I also came across normal forms while reading-up on a paper-'Generating Chaos in Continuous-Time Systems via Feedback Control' by Wang. I am still trying to understand the connection between normal forms and chaotification. If someone has any idea, this also would be very helpful.

 

[gtoguy97]

Unfortunately, there is no one single easy guide to transforming a system of differential equations into normal form. However, there are many resources available that can help you understand the process. For example, the book "Ordinary Differential Equations" by Morris W. Hirsch provides an excellent introduction to normal forms and their use in studying chaotic systems. It provides thorough explanations of the theory behind normal forms and discusses how they can be used to analyze the behavior of chaotic systems. The book also includes several examples of normal forms and how they are used in the analysis of chaotic systems.The book "Nonlinear Dynamics and Chaos" by Steven H. Strogatz also provides a comprehensive overview of normal forms and their use in studying chaotic systems. In addition to providing a comprehensive explanation of the theory behind normal forms, the book includes several examples of how normal forms can be used in practice. Finally, the website "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering" (https://nonlineardynamics.asu.edu/) provides a wealth of information on normal forms and their application to various areas of science and engineering. In particular, the website includes several tutorials on normal forms and their applications to chaotic systems. Overall, there is no single easy guide to transforming a system of differential equations into normal form. However, there are many resources available that can help you understand the process. By consulting these resources, you should be able to gain a better understanding of normal forms and how they can be used in the study of chaotic systems.