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On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z 3 Invariant Quintic Perturbations

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Abstract

A cubic system having three homoclinic loops perturbed by Z 3 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.

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Authors and Affiliations

  1. Department of Mathematics, Jiang Su University, Zhenjiang 212013, P. R. China

    Yu Hai Wu

  2. Department of Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

    Mao An Han

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  1. Yu Hai Wu
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  2. Mao An Han
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Correspondence to Yu Hai Wu.

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

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Wu, Y.H., Han, M.A. On the Bifurcations of a Hamiltonian Having Three Homoclinic Loops under Z 3 Invariant Quintic Perturbations. Acta Math Sinica 23, 869–878 (2007). https://doi.org/10.1007/s10114-005-0790-3

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  • DOI: https://doi.org/10.1007/s10114-005-0790-3

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