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On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems

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  • Ziguo Jiang

Abstract

We study the number of limit cycles for the quadratic polynomial differential systems , having an isochronous center with continuous and discontinuous cubic polynomial perturbations. Using the averaging theory of first order, we obtain that 3 limit cycles bifurcate from the periodic orbits of the isochronous center with continuous perturbations and at least 7 limit cycles bifurcate from the periodic orbits of the isochronous center with discontinuous perturbations. Moreover, this work shows that the discontinuous systems have at least 4 more limit cycles surrounding the origin than the continuous ones.

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  • Ziguo Jiang, 2016. "On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-11, September.
    • Handle: RePEc:hin:jnddns:4939780
    DOI: 10.1155/2016/4939780
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