中文摘要：

本文讨论一类分段非线性的不连续映射.首先通过数值仿真得到单参数的分岔图,发现该映射存在加周期序列和周期叠加序列.其次,分析了一个典型的周期n＋1解及迭代表达式;并推导了映射RLn序列周期n＋1解的边界碰撞分岔条件,通过数值仿真得到平面上RLn的周期区域全局分岔图.从而,我们验证该映射由于周期n＋1解的边界碰撞分岔形成了加周期序列和周期叠加序列.

英文摘要：

A class of discontinuous piecewise nonlinear maps are considered in the current paper. First of all,one- parameter bifurcation diagrams are obtained by numerical simulations. Then it is found that the maps have periodic adding sequences and periodic stacking sequences. Secondly,the typical periodic n ＋ 1 solutions and the iterative expressions are analyzed,and periodic n ＋ 1solution conditions of border collision bifurcation in the RLnsequences are deduced. Hence,the periodic regional global diagram in the RLnplane is obtained by the numerical simulation. Finally,it is verified that the map has periodic adding sequences and periodic stacking sequences due to border collision bifurcations of periodic n ＋ 1 solutions.