具有对称实焦点的分段线性类-Lienard系统的穿越周期轨

On the crossing periodic orbits of a piecewise linear Lienard-like system with symmetric admissible foci

摘要:

本文研究了具有对称实焦点的分段线性类-Lienard系统的穿越周期轨.通过把系统约化成一个有更少参数的正规形并构造左右子系统的 Poincare 映射, 本文证明了系统至少存在一个穿越周期轨.此外,本文还给出了一个系统不存在穿越周期轨的充分条件，并在在一定条件下对穿越周期轨的个数给出了一个上界.

Abstract:

We investigate the crossing periodic orbits of a piecewise linear Lienard-like system with symmetric admissible foci. By reducing the system to a normal form with less parameters and constructing the Poincare maps for the left and right subsystems, we show the existence of at least one crossing periodic orbit, give a sufficient condition for the non-existence of crossing periodic orbits, and provide an upper bound for the number of crossing periodic orbits under some conditions.