For a family of planar piecewise linear differential systems with two zones both having virtual foci, we investigate the appearance of limit cycles bifurcated from a global center (i.e. Poincaré bifurcations of limit cycles) when the discontinuity boundary is perturbed by the appearance of a nonregular point. Precisely, when the discontinuity boundary, which is a straight line, becomes two rays starting from the same point, we prove that accompanied by the birth of a limit cycle, the center either disappears or becomes local. So, our main results contain some sufficient conditions satisfied by the system parameters that guarantee the appearance of a limit cycle surrounding a period annulus. Moreover, our results provide a new method to design such a system having any number of limit cycles.

中文翻译：

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平面分段线性微分系统族不连续边界上非规则点引起的庞加莱分岔

对于具有两个具有虚拟焦点的区域的平面分段线性微分系统族，我们研究了当不连续边界受到非常规点的出现扰动时从全局中心分叉的极限环的出现（即极限环的庞加莱分岔） . 确切地说，当不连续边界，也就是一条直线，从同一点开始变成两条射线时，我们证明了伴随着极限环的诞生，中心要么消失，要么成为局部。因此，我们的主要结果包含系统参数满足的一些充分条件，这些条件保证在周期环周围出现极限环。此外，我们的结果提供了一种新方法来设计这种具有任意数量的极限环的系统。