基于Adomian分解法的分数阶非线性系统的分析及Lyapunov指数算法的实现

雷腾飞1,2,贺金满3,4,王艳玲1,臧红岩1,黄丽丽1,付海燕1

振动与冲击 ›› 2021, Vol. 40 ›› Issue (11) : 1-6.

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (11) : 1-6.
论文

基于Adomian分解法的分数阶非线性系统的分析及Lyapunov指数算法的实现

  • 雷腾飞1,2,贺金满3,4,王艳玲1,臧红岩1,黄丽丽1,付海燕1
作者信息 +

Analysis of fractional order nonlinear system based on Adomian decomposition method and realization of Lyapunov exponent algorithm

  • LEI Tengfei1,2, HE Jinman3,4, WANG Yanling1, ZANG Hongyan1, HUANG Lili1, FU Haiyan1
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摘要

针对分数阶Lü超混沌系统,采用Adomian分解法对其非线性项进行分解,并采用MATLAB软件绘制了系统的相图,同时从系统的分岔图、谱熵(spectral entropy,SE)复杂度、C0复杂度等数值仿真分析研究了0.90阶分数阶Lü超混沌系统丰富的动力学特性。同时采用QR分解算法,将Lyapunov指数计算展开,利用MATLAB软件仿真,得出Lyapunov指数谱与复杂度具有一致性的结论。

Abstract

Here, for a fractional order Lü hyperchaotic system, its nonlinear term was decomposed using Adomian decomposition method, and the system’s phase diagram was obtained with the software MATLAB.Then, abundant dynamic characteristics of a 0.90 order fractional order Lü hyperchaotic system were analyzed and studied with numerical simulation of the system’s bifurcation diagram, spectral entropy (SE) complexity, C0 complexity, etc.At the same time, QR decomposition was adopted to do expansion of Lyapunov exponent calculation.MATLAB was used to do simulation, it was shown that Lyapunov exponent spectrum is consistent with the complexity.

关键词

Adomian分解法 / 复杂度;分数阶混沌系统;Lyapunov指数算法

Key words

Adomian decomposition / complexity / fractional order chaotic system / Lyapunov exponent algorithm

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雷腾飞1,2,贺金满3,4,王艳玲1,臧红岩1,黄丽丽1,付海燕1. 基于Adomian分解法的分数阶非线性系统的分析及Lyapunov指数算法的实现[J]. 振动与冲击, 2021, 40(11): 1-6
LEI Tengfei1,2, HE Jinman3,4, WANG Yanling1, ZANG Hongyan1, HUANG Lili1, FU Haiyan1. Analysis of fractional order nonlinear system based on Adomian decomposition method and realization of Lyapunov exponent algorithm[J]. Journal of Vibration and Shock, 2021, 40(11): 1-6

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