混沌初步（英文版）
￥36.00定价
作者： 王震，惠小健
出版时间：2014年9月
出版社：西安电子科技大学出版社
- 西安电子科技大学出版社
- 9787560634555
- 130483
- 2014年9月
- 未分类
- 未分类
- O415.5
内容简介
《混沌初步(英文版)》由王震、惠小健著。This book includes four chapters, and mainly introduces the contents of the basic computational techniques of linear differential equation, the qualitative or geometric approaches for planar differential systems, the method of computation and analysis of the chaotic system, and several methods of feedback control, backstepping control and generalized synchronization for chaotic systems.
This book presents an introduction to chaos in dynamical system and fundamental theories of ordinary differential equations. It will be of interest to advance undergraduates in mathematics and graduate students in engineering taking courses in dynamical systems, nonlinear dynamics, nonlinear systems as well as chaos.
This book presents an introduction to chaos in dynamical system and fundamental theories of ordinary differential equations. It will be of interest to advance undergraduates in mathematics and graduate students in engineering taking courses in dynamical systems, nonlinear dynamics, nonlinear systems as well as chaos.
目录
CHAPTER 1 Computational Techniques of Linear Differential Equation
1.1 Basic concepts
1.2 First order linear differential equation
1.2.1 Separable equation
1.2.2 Linear equation
1.2.3 Exact equations and integrating factors
1.2.4 Direction fields
1.3 Second order differential equation
1.3.1 Homogeneous linear equation
1.3.2 Nonhomogeneous linear equation
1.4 First order differential equations
1.4.1 Basic theories of the first order DEs
1.4.2 Homogeneous linear DEs with constant coefficients
1.4.3 Nonhomogeneous linear DEs with constant coefficients
1.5 Three special methods
1.5.1 Laplace transform method
1.5.2 Power series method
1.5.3 Fourier series method
1.6 Numerical solution of differential equations
CHAPTER 2 Qualitative Analysis of Planar Differential Equations
2.1 Flow and manifold
2.1.1 Flow
2.1.2 Maniflod
2.2 Planar linear systems
2.3 Linearization of nonlinear systems
2.3.1 Singularities analysis of nonlinear systems
2.3.2 Stability of singularities
2.4 Periodic solutions of nonlinear systems
2.4.1 Orbit and limit set
2.4.2 Periodic orbit and limit cycle
2.5 Conservative system and dissipative system
2.5.1 Hamiltonian system
2.5.2 Dissipative systems
CHAPTER 3 Calculation and Analysis of Chaotic Systems
3.1 Attractor, Lyapunov exponent
3.1.1 Attractor
3.1.2 Lyapunov exponent
3.2 Center manifolds
3.2.1 Eigenspaces and manifolds
3.2.2 Center manifolds
3.3 Hopf bifurcation
3.3.1 Andronov-Hopf bifurcation
3.3.2 Hopf bifurcation of Lorenz-like system
3.4 Dimension reduction analysis
3.4.1 lnvariant algebraic surface
3.4.2 Invariant algebraic surface ofT system
3.5 Infinity analysis
3.5.1 Poincare compactification on R2 r
3.5.2 Poincare compactification on R3
3.6 Melnikov method
CHAPTER 4 Control and Synchronization of Chaotic Systems
4.1 Feedback control
4.1.1 Feedback control of T system
4.1.2 Differential feedback control of Jerk system
4.2 Backstepping control
4.2.1 Backstepping for strict feedbacl~ systems
4.2.2 Adaptive backstepping control of electromechanical system
4.2.3 Adaptive backstepping control of T system
4.3 Periodic parametric perturbation control
4.3.1 Periodic parametric perturbation system
4.3.2 Melnikov homoclinic orbits analysis
4.3.3 Melnikov periodic orbits analysis
4.3.4 Numerical experiments
4.4 Generalized synchronization
4.4.1 Preliminary
4.4.2 GS of fractional unified chaotic system
1.1 Basic concepts
1.2 First order linear differential equation
1.2.1 Separable equation
1.2.2 Linear equation
1.2.3 Exact equations and integrating factors
1.2.4 Direction fields
1.3 Second order differential equation
1.3.1 Homogeneous linear equation
1.3.2 Nonhomogeneous linear equation
1.4 First order differential equations
1.4.1 Basic theories of the first order DEs
1.4.2 Homogeneous linear DEs with constant coefficients
1.4.3 Nonhomogeneous linear DEs with constant coefficients
1.5 Three special methods
1.5.1 Laplace transform method
1.5.2 Power series method
1.5.3 Fourier series method
1.6 Numerical solution of differential equations
CHAPTER 2 Qualitative Analysis of Planar Differential Equations
2.1 Flow and manifold
2.1.1 Flow
2.1.2 Maniflod
2.2 Planar linear systems
2.3 Linearization of nonlinear systems
2.3.1 Singularities analysis of nonlinear systems
2.3.2 Stability of singularities
2.4 Periodic solutions of nonlinear systems
2.4.1 Orbit and limit set
2.4.2 Periodic orbit and limit cycle
2.5 Conservative system and dissipative system
2.5.1 Hamiltonian system
2.5.2 Dissipative systems
CHAPTER 3 Calculation and Analysis of Chaotic Systems
3.1 Attractor, Lyapunov exponent
3.1.1 Attractor
3.1.2 Lyapunov exponent
3.2 Center manifolds
3.2.1 Eigenspaces and manifolds
3.2.2 Center manifolds
3.3 Hopf bifurcation
3.3.1 Andronov-Hopf bifurcation
3.3.2 Hopf bifurcation of Lorenz-like system
3.4 Dimension reduction analysis
3.4.1 lnvariant algebraic surface
3.4.2 Invariant algebraic surface ofT system
3.5 Infinity analysis
3.5.1 Poincare compactification on R2 r
3.5.2 Poincare compactification on R3
3.6 Melnikov method
CHAPTER 4 Control and Synchronization of Chaotic Systems
4.1 Feedback control
4.1.1 Feedback control of T system
4.1.2 Differential feedback control of Jerk system
4.2 Backstepping control
4.2.1 Backstepping for strict feedbacl~ systems
4.2.2 Adaptive backstepping control of electromechanical system
4.2.3 Adaptive backstepping control of T system
4.3 Periodic parametric perturbation control
4.3.1 Periodic parametric perturbation system
4.3.2 Melnikov homoclinic orbits analysis
4.3.3 Melnikov periodic orbits analysis
4.3.4 Numerical experiments
4.4 Generalized synchronization
4.4.1 Preliminary
4.4.2 GS of fractional unified chaotic system
