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  

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

作　　者：雷腾飞 贺金满 王艳玲 臧红岩 黄丽丽 付海燕 LEI Tengfei;HE Jinman;WANG Yanling;ZANG Hongyan;HUANG Lili;FU Haiyan(Collaborative Innovation Center of Memristive Computing Application,QiluInstitute of Technology,Jinan 250200,China;Shandong Engineering Research Center of China-Germany Smart Factory Applied,Jinan 250200,China;College of Science,Zhongyuan University of Technology,Zhengzhou 451191,China;College of Aerospace Engineering Nanjing University of Aeronautics and Astronautics,Nangjing 210016,China)

机构地区：[1]齐鲁理工学院忆阻计算应用协同创新中心,济南250200 [2]山东省中德智慧工厂应用工程研究中心,济南250200 [3]中原工学院理学院,郑州451191 [4]南京航空航天大学航空宇航学院,南京210016

出　　处：《振动与冲击》2021年第11期1-6,共6页Journal of Vibration and Shock

基　　金：山东省重大科技创新工程项目(2019JZZY010111);山东省自然科学基金(ZR2017PA008);山东省重点研发计划(2019GGX104092);山东省高校科技计划(J18KA381);国家自然科学基金(61371163)。

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、C 0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。Here,for a fractional order Lühyperchaotic 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 Lühyperchaotic system were analyzed and studied with numerical simulation of the system’s bifurcation diagram,spectral entropy(SE)complexity,C 0 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 

分 类 号：O322[理学—一般力学与力学基础]