Singularity and Dynamics on Discontinuous Vector Fields 1st Edition by A C J Luo ISBN 0080480934 9780444527660

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Product details:

ISBN 10: 0080480934 
ISBN 13: 9780444527660
Author: A C J Luo

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.

Singularity and Dynamics on Discontinuous Vector Fields 1st Table of contents:

Chapter 1: Introduction
1.1 Smooth dynamics
1.2 Nonsmooth dynamics
1.3 Book layout
Chapter 2: Flow Passability and Tangential Flows
2.1 Domain accessibility
2.2 Discontinuous dynamic systems
2.3 Oriented boundary and singular sets
2.4 Local singularity and tangential flows
2.5 A piecewise linear system
2.6 A friction-induced oscillator
Chapter 3: Flow Switching Bifurcations
3.1 Set-valued vector fields
3.2 Switching bifurcations
3.3 Sliding fragmentation
3.4 Sliding conditions in a friction oscillator
3.5 Sliding criteria for a friction oscillator
Chapter 4: Transversal Singularity and Bouncing Flows
4.1 Transversal tangential flows
4.2 Cusped and inflexed tangential flows
4.3 Nonpassable tangential flows
4.4 Bouncing flows
4.5 A controlled piecewise linear system
Chapter 5: Real and Imaginary Flows
5.1 Singularity on boundary
5.2 Hyperbolicity and parabolicity
5.3 Boundary formation
5.4 Real flows
5.5 Imaginary flows
5.6 An example
Chapter 6: Discontinuous Vector Fields with Flow Barriers
6.1 Flow barriers
6.2 Switching bifurcations
6.3 Sliding fragmentation
6.4 A friction oscillator with flow barrier
Chapter 7: Transport Laws and Mapping Dynamics
7.1 Classification of discontinuity
7.2 Transport laws
7.3 Mapping dynamics
7.4 An impacting piecewise system
Chapter 8: Symmetry and Fragmentized Strange Attractor
8.1 Symmetric discontinuity
8.2 Switching sets and mappings
8.3 Grazing and mappings symmetry
8.4 Steady-state flow symmetry
8.5 Strange attractor fragmentation
8.6 Fragmentized strange attractors

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