摘要
A general method for a homoclinic loop of planar Hamiltonian systems to bifurcate two or three limit cycles under perturbations is established.Certain conditions are given under which the cyclicity of a homoclinic loop equals 1 or 2.As an application to quadratic systems,it is proved that the cyclicity of homoclinic loops of quadratic in-tegrable and non-Hamiltonian systems equals 2 except for one case.
A general method for a homoclinic loop of planar Hamiltonian systems to bifurcate two or three limit cycles under perturbations is established.Certain conditions are given under which the cyclicity of a homoclinic loop equals 1 or 2.As an application to quadratic systems,it is proved that the cyclicity of homoclinic loops of quadratic in-tegrable and non-Hamiltonian systems equals 2 except for one case.
基金
Project supported by the National Natural Science Foundation of China.
