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
本文研究了平面中的分段线性差异系统的家族，其两块被立方曲线隔开。通过分析获得的一阶Melnikov函数，我们给出了极限周期数的上限，这些限制是从$ n $ n $ n $ n $ dementer polyensigial扰动下的原点周围的周期环上分叉的。在$ n = 1 $和2的情况下，我们获得了分别有3和6的限制周期分别分叉。结果表明，开关曲线会影响极限周期的出现数量。
This paper studies the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. By analyzing the obtained first order Melnikov function, we give an upper bound of the number of limit cycles which bifurcate from the period annulus around the origin under $n$ degree polynomial perturbations. In the case $n=1$ and 2, we obtain that there have exactly 3 and 6 limit cycles bifurcating from the period annulus respectively. The result shows that the switching curves affect the number of the appearing of limit cycles.
