On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z_3 Invariant Quintic Perturbations  

On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z_3 Invariant Quintic Perturbations

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作  者:Yu Hal WU Mao An HAN 

机构地区:[1]Department of Mathematics, Jiang Su University, Zhenjiang 212013, P. R. China [2]Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

出  处:《Acta Mathematica Sinica,English Series》2007年第5期869-878,共10页数学学报(英文版)

基  金:The research is supported by fund of Youth of Jiangsu University(05JDG011)

摘  要:A cubic system having three homoclinic loops perturbed by Z3 invariant quintic polynomials is considered. By applying the qualitative method of differential equations and the numeric computing method, the Hopf bifurcation, homoclinic loop bifurcation and heteroclinic loop bifurcation of the above perturbed system are studied. It is found that the above system has at least 12 limit cycles and the distributions of limit cycles are also given.A cubic system having three homoclinic loops perturbed by Z3 invariant quintic polynomials is considered. By applying the qualitative method of differential equations and the numeric computing method, the Hopf bifurcation, homoclinic loop bifurcation and heteroclinic loop bifurcation of the above perturbed system are studied. It is found that the above system has at least 12 limit cycles and the distributions of limit cycles are also given.

关 键 词:homoclinic loop bifurcation heteroclinic loop bifurcation Hopf bifurcation stability limit cycles 

分 类 号:O174[理学—数学]

 

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