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On the number of limit cycles of a Z 4-equivariant quintic near-Hamiltonian system

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Abstract

In this paper, we study the number of limit cycles of a near-Hamiltonian system having Z 4-equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, 530003, P. R. China

    Xian Bo Sun

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

    Mao An Han

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  1. Xian Bo Sun
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  2. Mao An Han
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Correspondence to Mao An Han.

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Supported by National Natural Science Foundation of China (Grant Nos. 11271261, 11461001)

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Sun, X.B., Han, M.A. On the number of limit cycles of a Z 4-equivariant quintic near-Hamiltonian system. Acta. Math. Sin.-English Ser. 31, 1805–1824 (2015). https://doi.org/10.1007/s10114-015-2117-3

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  • DOI: https://doi.org/10.1007/s10114-015-2117-3

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