图书介绍
Bifurcation Theory of Limit Cycles 极限环分支理论PDF|Epub|txt|kindle电子书版本网盘下载
- Han Maoan 著
- 出版社： 北京：科学出版社发行部
- ISBN：9787030361400
- 出版时间：2013
- 标注页数：348页
- 文件大小：39MB
- 文件页数：357页
- 主题词：极限环－分枝－理论－英文
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图书目录
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