一类一维不连续分段光滑映射的加周期分岔

Period-adding bifurcations in a class of one-dimensional discontinuous piecewise smooth maps

摘要:

本文讨论了一类一维不连续的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所满足的条件；讨论了其形如$A^{m-1}B$的稳定$m$-周期轨($m\geqslant2$)的存在性，得到了此类周期轨存在及稳定时满足的参数条件，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。

Abstract:

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 $A^{m-1}B$. Analytical conditions for the existence and stability of such kind of periodic orbits are found. The period doubling and saddle-node bifurcations of those orbits are also studied.