正则化Filippov系统从类同宿联络分支到正则切奇点的极限环
On limit cycles in regularized Filippov systems bifurcating from homoclinic-like connections to regular-tangential singularities
摘要：
在本文中，我们关心的光滑的Filippov系统周围的同宿类连接到正则切奇点。我们提供的条件，以保证存在的极限环分叉从这样的连接。并给出了保证这种极限环稳定唯一的附加条件。所有的证明都是基于正则化Filippov系统在类同宿联络周围的第一个返回映射的构造。这样的地图是通过使用最近的本地行为的正规化Filippov系统周围的正则切向奇点的表征。不动点定理和Poincaré-Bendixson论证也被采用。
英文摘要：
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.
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