论文标题
通过扰动$ n $二维分段平滑差微分系统的分叉对周期轨道的分叉，并用两个开关平面
Bifurcation of periodic orbits by perturbing $n$-dimensional piecewise smooth differential systems with two switching planes
论文作者
论文摘要
在本文中，考虑了带有两个开关平面的分段平滑集成差分系统的一般扰动问题。首先，当不受干扰的系统具有周期性轨道家族时，可以得出一阶Melnikov向量函数，该功能可用于研究从Annuli时期分叉的周期性轨道数量。然后，通过使用获得的Melnikov矢量函数，我们获得了混凝土$ n $二维分段平滑差微分系统的周期性轨道数量的上限。
In this paper, the general perturbation problem of piecewise smooth integrable differential systems with two switching planes is considered. Firstly, when the unperturbed system has a family of periodic orbits, the first order Melnikov vector function is derived which can be used to study the number of periodic orbits bifurcated from the period annuli. Then, by using the obtained Melnikov vector function, we get an upper bound of the number of periodic orbits of a concrete $n$-dimensional piecewise smooth differential system.
