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Small-amplitude limit cycles of polynomial Liénard systems

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Abstract

In this paper, we study the number of limit cycles appeared in Hopf bifurcations of a Liénard system with multiple parameters. As an application to some polynomial Liénard systems of the form .x = y, .y = −g m (x) − f n (x)y, we obtain a new lower bound of maximal number of limit cycles which appear in Hopf bifurcation for arbitrary degrees m and n.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    MaoAn Han

  2. Department of Applied Mathematics, The University of Western Ontario, Ontario, N6A 5B7, Canada

    Yun Tian & Pei Yu

Authors
  1. MaoAn Han
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  2. Yun Tian
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  3. Pei Yu
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Correspondence to MaoAn Han.

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Han, M., Tian, Y. & Yu, P. Small-amplitude limit cycles of polynomial Liénard systems. Sci. China Math. 56, 1543–1556 (2013). https://doi.org/10.1007/s11425-013-4618-9

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  • DOI: https://doi.org/10.1007/s11425-013-4618-9

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