论文标题
关于从线性中心分叉的极限循环的数量，并具有代数切换曲线
On the number of limit cycles bifurcating from the linear center with an algebraic switching curve
论文作者
论文摘要
本文研究了飞机上的分段线性差异系统的家族，其两块由开关曲线隔开$ y = x^{m} $，其中$ m> 1 $是任意的正面。通过分析一阶Melnikov函数，我们给出了最大限制周期数的上限和下限，这些限制数量是从$ n $的多项式扰动下围绕原点周围的周期环分叉的。结果表明，切换曲线的程度会影响极限周期的数量。
This paper studies the family of piecewise linear differential systems in the plane with two pieces separated by a switching curve $y=x^{m}$, where $m>1$ is an arbitrary positive. By analysing the first order Melnikov function, we give an upper bound and an lower bound of the maximum number of limit cycles which bifurcate from the period annulus around the origin under polynomial perturbations of degree $n$. The results shows that the degree of switching curves affect the number of limit cycles.
