双侧增加的分段线性不连续映射的边界碰撞分岔
The Border-Collision Bifurcation in a Class of Discontinuous Maps with Two Linear Increasing Branches

利用Leonov方法研究了一类左右2侧都增加的分段线性不连续映射的动力学行为.通过调节系统的重要参数l,借助理论分析和数值仿真发现映射存在周期数成等差数列增长的加周期现象,也存在混沌和发散现象; 通过推导周期轨道的边界碰撞分岔曲线,确定了稳定周期轨道区域.根据高复杂度水平周期轨道的边界碰撞分岔曲线,结合双参数分岔图,解释了加周期现象和周期叠加现象.
Using theoretical analysis and numerical simulation,dynamic behavior of a class of discontinuous one-dimensional maps which are made of two linear increasing branches is considered by Leonov method.By modulating an important parameter of the map l,it is found that there exist the period adding sequences with period increasing of the arithmetic sequence,as well as chaos and divergence in the considered system.The boundaries of the stability region of the periodic orbits are determined by the border collision bifurcation curves of the periodic solutions.With the border collision bifurcation diagrams of periodic orbits of higher complexity levels,the phenomenon of period adding and period superposition are explained