2类墨西哥帽小波函数作用下的Logistic映射动力学

The effects of the two kinds of Mexican Hat wavelet function on the dynamics of Logistic map

目的研究墨西哥帽小波函数和不变顶点墨西哥帽小波函数对Logistic映射动力学的影响。方法基于理论分析与数值模拟相结合的方法,通过观察受调制之后的Logistic映射的分岔图,以及引进2个刻画分岔图的典型序参量,揭示2类墨西哥帽小波函数对Logistic映射的影响规律。结果这2类小波函数都能够使Logistic映射同时发生显著的拉伸和倍周期分岔点位置的改变现象。在大宽度调制作用下,不变顶点墨西哥帽小波函数对Logistic映射的影响会逐渐趋于一个稳定状态。通过对调制因子值域上下界的深入分析,揭示了这2类小波函数能够产生这种调制效果的潜在机理。结论墨西哥帽小波函数能够对Logistic映射动力学产生显著的影响。

Purposes—To study the influence of the Mexican Hat wavelet function and the invariant vertex Mexican Hat wavelet function on the dynamics of Logistic map.Methods—Based on theoretical analysis and numerical simulation,the influence rule of the two kinds of Mexican Hat wavelet function on the Logistic map are revealed by observing the bifurcation diagram of the modulated Logistic map and introducing two typical order parameters to characterize the bifurcation diagram.Result—It is found that the bifurcation diagram is significantly stretched and the positions of period-doubling bifurcation points are changed.Under the action of large width modulation,the influence of the invariant vertex Mexican Hat wavelet function on Logistic map tends to be stable.The potential modulation mechanism induced by the Mexican Hat wavelet function is revealed by analyzing the upper and lower bounds of the value domain of modulation factor.Conclusion—The Mexican Hat wavelet can impact the dynamics of Logistic map effectively.