分数阶立方映射的混沌行为  

Chaotic behavior of the fractional cubic map

作　　者：高仕龙[1,3] 余文慧 GAO Shi-Long;YU Wen-Hui(College of Mathematical and Physics,Leshan Normal University,Leshan 614000,China;School of Economics and Management,Jiangxi Agricultural University,Nanchang 330045,China;Research Centre of Applied Mathematics,Leshan Normal University,Leshan 614000,China)

机构地区：[1]乐山师范学院数理学院,乐山614000 [2]江西农业大学经济管理学院,南昌330045 [3]乐山师范学院应用数学研究中心,乐山614000

出　　处：《四川大学学报（自然科学版）》2024年第5期25-30,共6页Journal of Sichuan University(Natural Science Edition)

基　　金：四川省科技厅应用基础研究项目(2018JY0256);乐山师范学院校级重大项目(LZDP010)。

摘　　要：本文研究了分数阶立方映射的混沌特征.首先,在立方映射基础上,本文定义了分段常数分数阶微分方程,进而对其进行离散化处理得到分数阶立方映射.然后,通过研究映射的分岔和Lyapunov指数,本文揭示了分数阶立方映射通过倍周期分岔进入混沌,且相较传统立方映射具有更加丰富的混沌行为.此外本文还研究了更具普适性的时滞分数阶立方映射,发现该映射的混沌分岔点会随着参数的变化而变化.In this paper,the chaotic characteristics of fractional cubic map are investigated.Firstly,the fractional differential equation with piecewise constant elements is defined based on the cubic map,the fractional cubic map is obtained by using the discretization method.Then,by using the Lyapunov exponent and bifurcation diagram,it is revealed that the fractional cubic map enters chaos through the double-periodic bifurcation and its chaotic characteristics are more abundant than the traditional cubic map.Finally,a generalized delayed fractional cubic map is considered.It is shown that the chaotic bifurcation nodes of this map change with its parameters.

关 键 词：分数阶立方映射 混沌 时滞 LYAPUNOV指数 

分 类 号：O29[理学—应用数学]