A Multi-Interval Homotopy Analysis Method Using Multi-Objective Optimization for Analytically Analyzing Chaotic Dynamics in Memristive Circuit

Memristive nonlinear system has drawn much attention in recent years, due to its rich and complex dynamical characteristics. However, there are few studies focus on the analytical analysis of this significant system. In this paper, a novel analytical method for analyzing the chaotic trajectories of memristive circuit is proposed. This method combines Homotopy Analysis Method (HAM) and Multi-objective Optimization (MO), i.e., the convergence control parameter of traditional HAM is divided into lots of subintervals in the time domain and respectively optimized by MO, for accurately solving the Ordinary Differential Equations describing memristive circuits. Hence, this method is named by MO-based multi-interval HAM (MO-MIHAM). By using MO-MIHAM, we accurately tracked the chaotic trajectories of the classical Memristor-Capacitor-Inductor (MCL) circuit and current memristive Band Pass Filter (BPF) chaotic circuit. Furthermore, based on the comparisons of errors between analytical approximate solutions derived from MO-MIHAM and solutions solved by traditional homotopy-based analytical methods and by Runge-Kutta-Fehlberg Method (RKF45) based numerical analysis, we found that, MO-MIHAM is characterized by higher approximation accuracy and computational performance (comprehensively considering the accuracy, computational complexity and execution time by a proposed Quality Factor) among the homotopy-based analytical methods, due to the optimized convergence control parameters in subintervals. Besides this major advantage, MO-MIHAM enables both qualitative and quantitative analyses and high freedom to choose homotopy-related terms for simplicity, and it is insensitive to convergence issues. Therefore, it is a powerful tool for exploratory studies for analytically analyzing chaotic dynamics in memristive circuit.