Limit Cycles in a Family of Planar Piecewise Linear Differential Systems with a Nonregular Separation Line
Limit Cycles in a Family of Planar Piecewise Linear Differential Systems with a Nonregular Separation Line
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具有不规则分离线的平面分段线性微分系统族中的极限环
DOI：
10.1142/s0218127419501098
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发表时间：
2019-08
影响因子：
2.2
通讯作者：
Yang Xiao-Song
中科院分区：
文献类型：
--
作者：
Huan Song-Mei;Yang Xiao-Song
本文研究了一类平面分段线性微分系统的交叉极限环的个数，该系统的两个区域被从原点出发的两条射线所形成的非正则线所分隔.通过研究各子系统的动力学行为，对某些截面映射的参数表达式和主要性质进行了深入的研究。特别地，与分离线为直线的情况不同，证明了每个截面图可以由两个不同的部分分段，并且最多可以有一个拐点。此外，还得到了系统参数满足的拐点存在的充分必要条件。在此基础上，通过一个具有五个嵌套极限环的具体例子，验证了这些拐点在增加此类系统极限环最大数目方面所起的重要作用，其中两个极限环与一条分离线相交，另外三个极限环与两条分离线相交.因此，这里得到的五个极限环不同于现有文献中得到的所有极限环都穿过两条分离线。
In this paper, we investigate the number of crossing limit cycles in a family of planar piecewise linear differential systems with two zones separated by a nonregular line formed by two rays starting at the origin. By studying the dynamics of each subsystem, a thorough study including the parameteric expressions and main properties of some section maps is performed. Especially, different to the case with a straight separation line, it is proved that each section map can be piecewise with two different pieces and can have at most one inflection point. In addition to this, for the existence of these inflection points, some sufficient and necessary conditions satisfied by the system parameters are obtained. Based on these results, the importance played by these inflection points in increasing the maximum number of limit cycles in such systems is verified by providing a concrete example having five nested limit cycles with two crossing one separation ray and the other three crossing both separation rays. So, the five limit cycles obtained here are different from that obtained in the existing literature, where all the limit cycles cross both separation rays.
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影响因子：
1.1
作者：
E. Freire;E. Ponce;F. Torres
通讯作者：
E. Freire;E. Ponce;F. Torres
DOI：
10.1137/11083928x
发表时间：
2012-01
期刊：
SIAM J. Appl. Dyn. Syst.
影响因子：
--
作者：
E. Freire;E. Ponce;F. Torres
通讯作者：
E. Freire;E. Ponce;F. Torres
影响因子：
4
作者：
Coombes, S.;Thul, R.;Wedgwood, K. C. A.
通讯作者：
Wedgwood, K. C. A.
DOI：
10.1142/s0218127415500091
发表时间：
2014-05
期刊：
Int. J. Bifurc. Chaos
影响因子：
--
作者：
D. Novaes;E. Ponce
通讯作者：
D. Novaes;E. Ponce
DOI：
10.1016/j.physd.2016.07.008
发表时间：
2016-12
期刊：
Physica D: Nonlinear Phenomena
影响因子：
--
作者：
P. T. Cardin;Joan Torregrosa
通讯作者：
P. T. Cardin;Joan Torregrosa