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Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7

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  • Asheghi, R.
  • Bakhshalizadeh, A.

Abstract

In this paper, we first give the topological classification of level curves for a special Liénard system. Then we study the number of limit cycles of some polynomial Liénard systems with a cuspidal loop surrounded by a loop that is connected (homoclinic) to a nilpotent saddle. We prove that H(5,6)⩾9,H(6,6)⩾10 and H(7,6)⩾11, where H(m,n) is the maximal number of limit cycles in a Liénard system of type (m,n).

Suggested Citation

  • Asheghi, R. & Bakhshalizadeh, A., 2015. "Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 120-128.
    • Handle: RePEc:eee:chsofr:v:73:y:2015:i:c:p:120-128
    DOI: 10.1016/j.chaos.2015.01.009
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    References listed on IDEAS

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    1. Chao Liu & Maoan Han, 2013. "The Number of Limit Cycles of a Polynomial System on the Plane," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, July.
    2. Yang, Junmin & Han, Maoan, 2011. "Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 269-289.
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    Cited by:

    1. Yang, Junmin & Ding, Wei, 2018. "Limit cycles of a class of Liénard systems with restoring forces of seventh degree," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 422-437.

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