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The third order melnikov function of a cubic integrable system under quadratic perturbations

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  • Asheghi, R.
  • Nabavi, A.

Abstract

In this work, we consider a cubic integrable system under quadratic perturbations. We then study the limit cycles of the perturbed system by using Melnikov functions up to order three. We prove that the sharp upper bound of the number of limit cycles lies between six and seven. Also, we give an example that shows six limit cycles.

Suggested Citation

  • Asheghi, R. & Nabavi, A., 2020. "The third order melnikov function of a cubic integrable system under quadratic perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920306871
    DOI: 10.1016/j.chaos.2020.110291
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    References listed on IDEAS

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    1. Buică, Adriana & Llibre, Jaume, 2007. "Limit cycles of a perturbed cubic polynomial differential center," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1059-1069.
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    Cited by:

    1. Yanwei Liu & Tonghua Zhang & Xia Liu, 2022. "Third Order Melnikov Functions of a Cubic Center under Cubic Perturbations," Mathematics, MDPI, vol. 10(11), pages 1-17, May.

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