基于Adomian分解法的含有3个正Lyapunov指数分数阶混沌系统的仿真分析  

SIMULATION ANALYSIS OF FRACTIONAL-ORDER CHAOTIC SYSTEM WITH THREE POSITIVE LYAPUNOV EXPONENTS BASED ON ADOMIAN DECOMPOSITION METHOD

作　　者：雷腾飞 付海燕 张艳萍 张鑫 LEI Tengfei;FU Haiyan;ZHANG Yanping;ZANG Xin(School of Mechanical and Electrical Engineering.Qilu lnstitute of Technology Shandong,Jinan 250200,China;School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing 210023,China)

机构地区：[1]齐鲁理工学院机电工程学院,济南250200 [2]南京财经大学应用数学学院,南京210023

出　　处：《内蒙古农业大学学报（自然科学版）》2020年第6期89-95,共7页Journal of Inner Mongolia Agricultural University(Natural Science Edition)

基　　金：国家自然科学基金项目(61371163);山东省自然科学基金(ZR2017PA008);山东省高校科技计划项目(J18KA381)。

摘　　要：基于Adomian分解法研究了一类含有3个正Lyapunov指数的分数阶混沌系统。从Adomian表达式出发,对分数阶五维混沌系统进行了非线性项的分解,同时采用Matlab软件通过分析系统分岔图、Lyapunov指数谱、复杂度以及吸引子相图等特征,阐述了分数阶混沌系统丰富的动力学特性。仿真结果表明,系统在混沌区的复杂性会随着分数阶阶数q值减小而增大,仿真结果为分数阶混沌系统应用于加密提供了理论支撑。A class of fractional order chaotic systems with three positive Lyapunov exponents were studied based on the Adomian decomposition method in this paper.Starting from the Adomian expression,the nonlinear term of fractional order five-dimensional chaotic system was decomposed.At the same time,the rich dynamic characteristics of fractional order chaotic system were expounded by analyzing the bifurcation diagram,Lyapunov exponent spectrum,complexity and attractor phase diagram of the system by using the Matlab software.The simulation results showed that the complexity of the system in the chaotic region increased with the q value decreasing.The results provided theoretical supports for the application of fractional-order chaotic system to encryption.

关 键 词：ADOMIAN分解法 分数阶混沌系统 复杂度 LYAPUNOV指数谱 

分 类 号：O322[理学—一般力学与力学基础]