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一類混沌動力系統的分歧分析與控制—分歧分析與控制(英文) 版權信息
- ISBN：9787560398136
- 條形碼：9787560398136 ; 978-7-5603-9813-6
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>
一類混沌動力系統的分歧分析與控制—分歧分析與控制(英文) 內容簡介
本書是一部英文版的非線性科學方面的專著。本書介紹了三個不同類型的分歧的分析與數值的研究.類屬于局部分歧的是霍普夫分歧，另外兩個類型是同宿與異宿分歧，屬于全局分歧.還討論了兩個不同的帶時滯反饋控制的非線性動力系統中的分歧分析與混沌.在本書中，我們使用了有力的工具和重要的理論標準（比如，待定系數法、互補群群際能量壁壘準則、李雅普諾夫系數、席爾尼科夫(Si''''lnikov)準則、中心流形理論、卡當公式、笛卡兒特號法則和時滯反饋控制)，從而引入一個L山系統中的霍普夫分歧的局部分析，還有席爾尼科夫軌道存在的全局分析，以及斯梅爾馬蹄和Lǘ系統中的馬蹄型混沌，Zhou系統和僅具有兩個穩定的結點一焦，點的3一D混沌系統.此外，將使用時滯反饋控制來控制Zhou系統和Schimizu-Morioka系統。
一類混沌動力系統的分歧分析與控制—分歧分析與控制(英文) 目錄
(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
編輯手記
(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
編輯手記
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