Bifurcation Theory of Limit Cycles 极限环分支理论【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

Bifurcation Theory of Limit Cycles 极限环分支理论PDF格式电子书版下载

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Chapter 1 Limit Cycle and Its Perturbations1

1.1 Basic notations and facts1

1.2 Further discussion on property of limit cycles7

1.3 Perturbations of a limit cycle13

Chapter 2 Focus Values and Hopf Bifurcation20

2.1 Poincarémap and focus value20

2.2 Normal form and Poincaré-Lyapunov technique28

2.3 Hopf bifurcation near a focus and systems with symmetry44

2.4 Degenerate Hopf bifurcation near a center58

2.5 Hopf bifurcation for Liénard systems72

2.6 Hopf bifurcation for some polynomial systems92

Chapter 3 Perturbations of Hamiltonian Systems106

3.1 General theory106

3.2 Limit cycles near homoclinic and heteroclinic loops124

3.3 Finding more limit cycles by Melnikov functions163

3.4 Limit cycle bifurcations near a nilpotent center183

3.5 Limit cycle bifurcations with a nilpotent cusp200

3.6 Limit cycle bifurcations with a nilpotent saddle214

Chapter 4 Stability of Homoclinic Loops and Limit Cycle Bifurcations254

4.1 Local behavior near a saddle254

4.2 Stability of a homoclinic loop and bifurcation near it269

4.3 Homoclinic and heteroclinic bifurcations in near-Hamiltonian systems290

Chapter 5 The Number of Limit Cycles of Polynomial Systems310

5.1 Introduction310

5.2 Some fundamental results312

5.3 Further study for general polynomial systems322

Bibliography333

Index347