(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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