作者：（英文）埃尔-哈提卜·苏比·阿里·埃尔-
页数：189
出版社：哈尔滨工业大学出版社
出版日期：2022
ISBN：9787560398136
电子书格式：pdf/epub/txt
内容简介
本书是一部英文版的非线性科学方面的专著。本书介绍了三个不同类型的分歧的分析与数值的研究.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.在本书中，我们使用了有力的工具和重要的理论标准（比如，待定系数法、互补群群际能量壁垒准则、李雅普诺夫系数、席尔尼科夫(Si””lnikov)准则、中心流形理论、卡当公式、笛卡儿特号法则和时滞反馈控制)，从而引入一个L山系统中的霍普夫分歧的局部分析，还有席尔尼科夫轨道存在的全局分析，以及斯梅尔马蹄和Lǘ系统中的马蹄型混沌，Zhou系统和仅具有两个稳定的结点一焦，点的3一D混沌系统.此外，将使用时滞反馈控制来控制Zhou系统和Schimizu-Morioka系统。
目录
(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
编辑手记
(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
编辑手记
