论文标题
正规化Filippov系统中的极限循环，从类似于同型的连接到常规区分奇异性的分叉
On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
论文作者
论文摘要
在本文中，我们担心在类似于常规的奇异点上的类似于斜角的连接周围的Filippov系统。我们提供条件，以确保从这种连接中分叉的极限周期存在。还提供了其他条件，以确保这种极限周期的稳定性和独特性。所有的证明都是基于围绕同型连接的正规化Filippov系统的第一返回地图的构建。通过使用近期正规界奇点的正规化Filippov系统的局部行为的最新表征获得这样的图。还采用了固定点定理和庞加莱·奔驰的论点。
In this paper, we are concerned about smoothing of Filippov systems around homoclinic-like connections to regular-tangential singularities. We provide conditions to guarantee the existence of limit cycles bifurcating from such connections. Additional conditions are also provided to ensured the stability and uniqueness of such limit cycles. All the proofs are based on the construction of the first return map of the regularized Filippov system around homoclinic-like connections. Such a map is obtained by using a recent characterization of the local behaviour of the regularized Filippov system around regular-tangential singularities. Fixed point theorems and Poincaré-Bendixson arguments are also employed.
