一类不连续映射的边界碰撞分岔分析  

Border Collision Bifurcation in a Class of Discontinuous Maps

作　　者：诸葛得莉 李群宏[1] 

机构地区：[1]广西大学数学与信息科学学院,南宁530004

出　　处：《琼州学院学报》2015年第5期6-9,共4页Journal of Qiongzhou University

基　　金：国家自然科学基金项目(No.11372077)

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.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.

关 键 词：不连续映射 周期n+1解 边界碰撞分岔 加周期序列 周期叠加序列 

分 类 号：O189.1[理学—数学]