On the Limit Cycles for Continuous and Discontinuous Cubic Differential Systems

Ziguo Jiang

Discrete Dynamics in Nature and Society, 2016, vol. 2016, issue 1

Abstract: We study the number of limit cycles for the quadratic polynomial differential systems x˙=-y+x2, y˙=x+xy 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.

Date: 2016
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https://doi.org/10.1155/2016/4939780

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnddns:v:2016:y:2016:i:1:n:4939780

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