(I) Summary(II) Aim of the study(III) IntroductionChapter 1: Nonlinear Dynamical Systems and Preliminaries.1.1 Nonlinear dynamical systems1.1.1 Continuous dynamical systems1.1.2 Equilibrium points of dynamical system1.2 Attractor1.2.1 Strange attractor1.2.2 Limit cycle1.3 Bifurcations1.3.1 Saddle-node bifurcation1.3.2 Transcritical bifurcation1.3.3 The Pitchfork bifurcation1.3.4 Hopfbifurcation1.4 Global bifurcations1.4.1 A Homoclinic Bifurcation1.4.2 Heteroclinic Bifurcation1.5 Chaos1.6 Lyapunov exponents1.7 Time-delayed feedback method1.7.1 Hopfbifurcation in delayed systems1.7.2 Center manifold theoryChapter 2: LOCAL BIFURCATION On Hopfbifurcation of Liu chaotic system2.1 Introduction2.2 Dynamical analysis of the Liu system2.3 The first Lyapunov coefficient2.4 The Hopf-bifurcation analysis of Liu systemChapter 3: GLOBAL BIFURCATION Existence of heteroclinic and homoclinic orbits in two different chaotic dynamical systems3.1 Introduction3.2 Homoclinic and Heteroclinic orbit3.3 Structure of the Lii system3.4 The existence ofheteroclinic orbits in the Lu3.4.1 Finding heteroclinic orbits3.4.2 The uniform convergence ofheteroclinic orbits series expansion3.5 Structure of the Zhou‘s system3.6 Existence of Si’lnikov-type orbits3.6.1 The existence ofheteroclinic orbits3.6.2 The uniform convergence ofheteroclinic orbits series expansion.3.7 The existence ofhomoclinic orbitsChapter 4: Si‘lnikov Chaos of a new chaotic attractor from General Lorenz system family4.1 Introduction4.2 The novel system and its dynamical analysis4.3 The existence ofheteroclinic orbits in the novel system4.4 The uniform convergence of heteroclinic orbits series expansion4.5 The existence ofhomoclinic orbits4.6 The uniform convergence ofhomoclinic orbits series ExpansionChapter 5: Bifurcation Analysis and Chaos Control in Zhou’s System and Schimizu-Morioka system with Delayed Feedback5.1 Introduction5.2 Bifurcation analysis of Zhous system with delayed feedback force5.3 Direction and stability of Hopfbifurcation5.4 Numerical results5.5 Bifurcation Analysis and Chaos Control in Schimizu- Morioka Chaotic with Delayed Feedback5.5.1 Bifurcation analysis of Schimizu-Morioka system with delayed feedback force5.5.2 Direction and stability of Hopfbifurcation.5.5.3 Numerical resultsRecommendations: Bibliography编辑手记
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