本书是一部英文版的非线性科学方面的专著，内容是20世纪中非常令人鼓舞的非线性科学。它不仅在科学和技术上对人类有非常大的震撼而且还在世界观和方法论层面对世人造成了颠覆式的冲击。 本书介绍了三个不同类型的分歧的分析与数值的研究。第一类属于局部分歧的是霍普夫分歧，另外两个类型是同宿与异宿分歧，属于全局分歧。还讨论了两个不同的带时滞反馈控制的非线性动力系统中的分歧分析与混沌。

(I) Summary
(II) Aim of the study
(III) Introduction
Chapter 1: Nonlinear Dynamical Systems and Preliminaries.
1.1 Nonlinear dynamical systems
1.1.1 Continuous dynamical systems
1.1.2 Equilibrium points of dynamical system
1.2 Attractor
1.2.1 Strange attractor
1.2.2 Limit cycle
1.3 Bifurcations
1.3.1 Saddle-node bifurcation
1.3.2 Transcritical bifurcation
1.3.3 The Pitchfork bifurcation
1.3.4 Hopfbifurcation
1.4 Global bifurcations
1.4.1 A Homoclinic Bifurcation
1.4.2 Heteroclinic Bifurcation
1.5 Chaos
1.6 Lyapunov exponents
1.7 Time-delayed feedback method
1.7.1 Hopfbifurcation in delayed systems
1.7.2 Center manifold theory
Chapter 2: LOCAL BIFURCATION On Hopfbifurcation of Liu chaotic system
2.1 Introduction
2.2 Dynamical analysis of the Liu system
2.3 The first Lyapunov coefficient
2.4 The Hopf-bifurcation analysis of Liu system
Chapter 3: GLOBAL BIFURCATION Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems
3.1 Introduction
3.2 Homoclinic and Heteroclinic orbit
3.3 Structure of the Lii system
3.4 The existence ofheteroclinic orbits in the Lu
3.4.1 Finding heteroclinic orbits
3.4.2 The uniform convergence ofheteroclinic orbits series expansion
3.5 Structure of the Zhou's system
3.6 Existence of Si'lnikov-type orbits
3.6.1 The existence ofheteroclinic orbits
3.6.2 The uniform convergence ofheteroclinic orbits series expansion.
3.7 The existence ofhomoclinic orbits
Chapter 4: Si'lnikov Chaos of a new chaotic attractor from General Lorenz system family
4.1 Introduction
4.2 The novel system and its dynamical analysis
4.3 The existence ofheteroclinic orbits in the novel system
4.4 The uniform convergence of heteroclinic orbits series expansion
4.5 The existence ofhomoclinic orbits
4.6 The uniform convergence ofhomoclinic orbits series Expansion
Chapter 5: Bifurcation Analysis and Chaos Control in Zhou's System and Schimizu-Morioka system with Delayed Feedback
5.1 Introduction
5.2 Bifurcation analysis of Zhou's system with delayed feedback force
5.3 Direction and stability of Hopfbifurcation
5.4 Numerical results
5.5 Bifurcation Analysis and Chaos Control in Schimizu- Morioka Chaotic with Delayed Feedback
5.5.1 Bifurcation analysis of Schimizu-Morioka system with delayed feedback force
5.5.2 Direction and stability of Hopfbifurcation.
5.5.3 Numerical results
Recommendations: Bibliography
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