一类不连续映射的分岔分析

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.