本书主要介绍了对三个不同类型混沌动力系统的分歧的分析与数值研究，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。本书由五章组成：第一章介绍了非线性动力系统的一些基本知识；第二章通过使用互补群群际能量壁垒准则（CCEBC）分析了刘系统的动力行为；第三章对待定系数方法进行了研究；第四章介绍了对新3-D混沌系统中的希尔尼科夫同宿轨道和异宿轨道的存在性的分析研究；最后一章研究了具有时滞反馈控制的系统中的局部霍普夫分歧。
(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
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