Limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems
Limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems
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DOI：
10.1016/j.jde.2018.07.016
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发表时间：
2017-05
影响因子：
2.4
通讯作者：
Xiuli Cen;Lijun Yang;Meirong Zhang
中科院分区：
文献类型：
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作者：
Xiuli Cen;Lijun Yang;Meirong Zhang
本文研究了具有间断直线x= 0的任意次分段多项式微分系统内部的二次等距中心扰动。主要考虑的是一阶Melnikov函数的零点个数和从周期环分叉出的极限环个数的估计。对于二次等距中心S1，S2和S3，我们将给出一阶Melnikov函数零点个数的精确上界.对于二次等距中心S4，我们给出了一个粗略的估计.然而，当问题是减少到多项式微分系统内的扰动，我们的结果为S 4将改善李等人。（2000年）[12]。此外，我们还揭示了一阶Melnikov函数法和一阶平均法在研究分段多项式微分系统极限环个数时的等价性。
In this paper, we consider the quadratic isochronous centers perturbed inside piecewise polynomial differential systems of arbitrary degree n with the straight line of discontinuity x= 0. The main concerns are the number of zeros of the first order Melnikov functions and the estimate of the number of limit cycles bifurcating from the period annuli. For quadratic isochronous centers S 1, S 2 and S 3, we will provide a sharp upper bound for the number of zeros of the first order Melnikov functions. For quadratic isochronous center S 4, we give a rough estimate. However, when the problem is reduced to perturbations inside polynomial differential systems, our result for S 4 will improve that in Li et al.(2000)[12] significantly. Moreover, we will reveal out some equivalence between the first order Melnikov function method and the first order averaging method for investigating the number of limit cycles of piecewise polynomial differential systems.