This book introduces the bifurcation theory of limit cycles of planar systems with multiple parameters.It is focused on the most recent developments in this field and provides major advances in fundamental theory of limit cycles.The main topics include Hopf bifurcation of limit cycles from a center or a focus,homoclinic bifurcations near a homoclinic or a heteroclinic loop,and the number of limit cycle in global bifurcations of near-Hamiltonian polynomial systems of arbitrary degree.This book will be of use to graduate mathematics students as well as scientists. Han Maoan is a professor at the Institute of Mathematical Sciences of Shanghai Normal University.He has been working on the research of differential equations and dynamical systems for 30 years with 300 papers published.
样章试读
暂时还没有任何用户评论
全部咨询(共0条问答)
暂时还没有任何用户咨询内容
目录
Preface Chapter 1 Limit Cycle and Its Perturbations 1.1 Basic notations and facts 1.2 Further discussion on property of limit cycles 1.3 Perturbations of a limit cycle Chapter 2 Focus Values and Hopf Bifurcation 2.1 Poincaré map and focus value 2.2 Normal form and Poincaré-Lyapunov technique 2.3 Hopf bifurcation near a focus and systems with symmetry 2.4 Degenerate Hopf bifurcation near a center 2.5 Hopf bifurcation for Li?enard systems 2.6 Hopf bifurcation for some polynomial systems Chapter 3 Perturbations of Hamiltonian Systems 3.1 General theory 3.2 Limit cycles near homoclinic and heteroclinic loops 3.3 Finding more limit cycles by Melnikov functions 3.4 Limit cycle bifurcations near a nilpotent center 3.5 Limit cycle bifurcations with a nilpotent cusp 3.6 Limit cycle bifurcations with a nilpotent saddle Chapter 4 Stability of Homoclinic Loops and Limit Cycle Bifurcations 4.1 Local behavior near a saddle 4.2 Stability of a homoclinic loop and bifurcation near it 4.3 Homoclinic and heteroclinic bifurcations in near-Hamiltonian systems Chapter 5 The Number of Limit Cycles of Polynomial Systems 5.1 Introduction 5.2 Some fundamental results 5.3 Further study for general polynomial systems Bibliography Index