Basin of Attraction Analysis of New Memristor-Based Fractional-Order Chaotic System

Long Ding,Fei Yu,Li Cui,Jie Jin,Guillermo Huerta Cuellar

doi:10.1155/2021/5578339

Abstract

Memristor is the fourth basic electronic element discovered in addition to resistor, capacitor, and inductor. It is a nonlinear gadget with memory features which can be used for realizing chaotic, memory, neural network, and other similar circuits and systems. In this paper, a novel memristor-based fractional-order chaotic system is presented, and this chaotic system is taken as an example to analyze its dynamic characteristics. First, we used Adomian algorithm to solve the proposed fractional-order chaotic system and yield a chaotic phase diagram. Then, we examined the Lyapunov exponent spectrum, bifurcation, SE complexity, and basin of attraction of this system. We used the resulting Lyapunov exponent to describe the state of the basin of attraction of this fractional-order chaotic system. As the local minimum point of Lyapunov exponential function is the stable point in phase space, when this stable point in phase space comes into the lowest region of the basin of attraction, the solution of the chaotic system is yielded. In the analysis, we yielded the solution of the system equation with the same method used to solve the local minimum of Lyapunov exponential function. Our system analysis also revealed the multistability of this system.

Highlights

After theoretic derivation of the relationships between the four basic electrical physical quantities—voltage, current, charge, and magnetic flux—Cai assumed that there exists a fourth basic circuit element: the memristor
Results show that memristor-based chaotic circuits provide a greater variety of dynamic behaviors
As memristors are nanoelements which are not commercialized yet, in the current studies related to conventional memristorbased chaotic circuits, researchers tend to use existing simulation analog elements to realize a memristor analog circuit and use it to investigate the dynamic properties of the designed system

Summary

Introduction

Chaotic systems have attracted wide attention from researchers due to their own particularities and their vast application potential in the memristor [1,2,3,4], random number generator [5, 6], secure communication [7,8,9], image encryption [10,11,12,13,14], and artificial neural network [15,16,17,18,19,20]. E purpose of this research is to take the analysis on the proposed chaotic system as an example to exhibit the nonlinear dynamical behavior of a memristor-based fractional-order chaotic system and to provide a new theoretical basis for the study of nonlinear systems.

Results

Conclusion