Dynamics and Complexity Analysis of Fractional-Order Chaotic Systems with Line Equilibrium Based on Adomian Decomposition

Abstract

In this paper, the Adomian decomposition method (ADM) is applied to solve the fractional-order system with line equilibrium. The dynamics of the system is analyzed by means of the Lyapunov exponent spectrum, bifurcations, chaotic attractor, and largest Lyapunov exponent diagram. At the same time, through the Lyapunov exponent spectrum and bifurcation graph of the system under the change of the initial value, the influence of fractional order q on the system state can be observed. That is, integer-order systems do not have the phenomenon of attractors coexistence, while fractional-order systems have it.