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

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (11) : 1-6.

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

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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.

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

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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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