Singularity and Dynamics on Discontinuous Vector Fields

This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones’ thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics.

Challenging continuous Newton's dynamicsOriginal theory and seeds of new researches in the fieldWide spectrum of applications in science and engineeringSystematic presentation and clear illustrations

Chapter 1: Introduction

Chapter 2: Flow Passability and Tangential Flows

Chapter 3: Flow Switching Bifurcations

Chapter 4: Transversal Singularity and Bouncing Flows

Chapter 5: Real and Imaginary Flows

Chapter 6: Discontinuous Vector Fields with Flow Barriers

Chapter 7: Transport Laws and Mapping Dynamics

Chapter 8: Symmetry and Fragmentized Strange Attractor

Appendix A

Reference

Index