一维不连续分段光滑映射的加周期分岔

Period-adding bifurcations in one-dimensional discontinuous piecewise smooth maps

本文讨论了一类一维不连续非线性分段光滑映射的动力学行为,得到了其不动点存在和稳定时参数应满足的条件,讨论了其形如Am-1 B的稳定m-周期轨(m≥2)的存在性,得到了此类周期轨存在及稳定时的参数条件,并进一步讨论了这些周期轨的倍周期分岔和鞍结点分岔现象.

In this paper, we consider the dynamics of a class of one-dimensional discontinuous nonlinear maps. We obtain the existence and stability conditions of fixed points in the parameter space. Then we study the existence and stability of period-m orbit of type Am-1B. Analytical conditions for the existence and stability of the periodic orbits are found. The period doubling and saddle-node bifurcations of the or- bits are also considered.