Many natural phenomena can be modeled as discontinuous dynamical systems separated by a nonregular line. The number and distribution of limit cycles in discontinuous linear systems are important topics for research. In this paper, we focus on the limit cycles created by discontinuous planar piecewise linear systems separated by a nonregular line of center–center type, and prove that such systems have at most two limit cycles, which can be reached. Furthermore, the two limit cycles are nested and intersect the separation line at two points or four points, that is, either both intersect the separation line at two points or one intersects the separation line at two points and the other one at four points.

中文翻译：

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由中心-中心型非规则线分隔的不连续平面分段线性系统中的极限环

许多自然现象可以建模为由一条不规则线分隔的不连续动力系统。不连续线性系统中极限环的数量和分布是重要的研究课题。在本文中，我们关注由不连续的平面分段线性系统创建的极限环，这些系统由中心-中心型不规则线隔开，并证明此类系统最多有两个极限环，可以达到。此外，两个极限环嵌套并与分隔线相交于两点或四点，即要么都与分隔线两点相交，要么一个与分隔线两点相交，另一个与分隔线四点相交。