一类二次等时微分系统在不连续二次多项式扰动下的极限环分支

Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (5): 919-927.

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Limit Cycles for Perturbing Quadratic Isochronous Center Inside Discontinuous Quadratic Polynomial Differential System

Li Shimin¹, Cen Xiuli²

1. School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou 510320;
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084

Received:2015-12-24 Revised:2016-06-12 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC (11401111, 11171355)

Abstract

Abstract:

In this paper, we bound the number of limit cycles which bifurcate from the period annulus of a class of quadratic isochronous center ?=-y-(4)/(3)x²,?=x-(16)/(3)xy, when perturbed inside the class of all discontinuous quadratic polynomial differential systems. Our results show that there are at most 4 limit cycles bifurcating from this system. Moreover, this bound is sharp.

Key words: Limit cycle, Discontinuous differential system, Averaging method, Quadratic isochronous center

CLC Number:

O175

Li Shimin, Cen Xiuli. Limit Cycles for Perturbing Quadratic Isochronous Center Inside Discontinuous Quadratic Polynomial Differential System[J].Acta mathematica scientia,Series A, 2016, 36(5): 919-927.

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Limit Cycles for Perturbing Quadratic Isochronous Center Inside Discontinuous Quadratic Polynomial Differential System

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