一类不连续映射的分岔分析  

BIFURCATION ANALYSIS IN A CLASS OF DISCONTINUOUS MAPS

作　　者：李群宏[1] 韦丽梅[1] 卢裕木 

机构地区：[1]广西大学数学与信息科学学院,南宁530004

出　　处：《动力学与控制学报》2015年第4期271-277,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10972059和11372077);广西自然科学基金资助项目(2010GXNSFA013110和2013GXNSFAA019017)~~

摘　　要：研究一类一维分段不连续映射的边界碰撞分岔问题,推导了周期n解的边界碰撞分岔曲线及fold分岔条件,通过数值仿真验证了这些条件的正确性.研究发现系统存在周期增加序列和周期叠加序列.最后,对分段不连续映射进行三参数分岔研究,揭示了系统各参数对其动力学行为的综合影响.Border-collision bifurcations of a class of one-dimensional piecewise discontinuous maps were investi- gated. The border-collision bifurcation curves and fold bifurcation conditions for period-n solutions were derived. The correctness of the deduced results was confirmed through the numerical simulations. It is found that there are period adding sequences and period overlapping sequences in the system. Finally, the three-parameter bifurca- tions of the piecewise discontinuous map were considered, which demonstrates the combined influence of all the parameters in the map.

关 键 词：分段映射 边界碰撞分岔 周期叠加 周期增加 

分 类 号：O313.4[理学—一般力学与力学基础]