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

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.