Adomian Decomposition Algorithm for Studying Incommensurate Fractional-Order Memristor-Based Chua’s System

Abstract

Based on the definitions of fractional-order differential and Adomian decomposition algorithm, the numerical approximate solution of the incommensurate fractional-order memristor-based Chua’s system is investigated. Dynamical characteristics of the proposed system are studied by using phase diagram, bifurcation analysis and power spectrum. Research results show that compared with the Adams–Bashforth–Moulton algorithm, the Adomian decomposition algorithm yields more accurate results and its solution generally converges more rapidly. Compared with 3.776 achieved by the Adams–Bashforth–Moulton algorithm, the minimum order of the incommensurate fractional-order memristor-based Chua’s system solved by using Adomian decomposition algorithm is 1.76, which is much smaller. A reliable and efficient binary test for chaos, called “0–1 test”, is utilized to detect the presence of chaotic attractors in the system dynamics.