Characteristic Analysis of Fractional-Order Memristor-Based Hypogenetic Jerk System and Its DSP Implementation

Chuan Qin,Kehui Sun,Shaobo He

doi:10.3390/electronics10070841

Abstract

In this paper, a fractional-order memristive model with infinite coexisting attractors is investigated. The numerical solution of the system is derived based on the Adomian decomposition method (ADM), and its dynamic behaviors are analyzed by means of phase diagrams, bifurcation diagrams, Lyapunov exponent spectrum (LEs), dynamic map based on SE complexity and maximum Lyapunov exponent (MLE). Simulation results show that it has rich dynamic characteristics, including asymmetric coexisting attractors with different structures and offset boosting. Finally, the digital signal processor (DSP) implementation verifies the correctness of the solution algorithm and the physical feasibility of the system.

Highlights

Chaotic systems have initial sensitivity, long-term unpredictability and other excellent characteristics; they can be cross-combined with other scientific fields such as biology, information science, security, and engineering [1,2,3,4,5]
Set a = 0.4, while q and other parameters remain unchanged, We studied the influence of parameter c on system behavior
There are four chaotic attractors with different structures and five periodic attractors. It illustrates the multiple stability of the system, and it is just a dynamic characteristic exhibited by a few sample points in the initial value space

Summary

Introduction

Chaotic systems have initial sensitivity, long-term unpredictability and other excellent characteristics; they can be cross-combined with other scientific fields such as biology, information science, security, and engineering [1,2,3,4,5]. A new memristive chaotic circuit was obtained by replacing the non-linear resistor with a memristor in a chaotic circuit [17,18,19,20] Most of these studies are based on integer-order calculus systems. 2. Solution of the Fractional-Order Memristor-Based Hypogenetic Jerk System 2.1. Through replacing the newly proposed memristor featured by W(φ) = α + 3βφ and introducing fractional calculus into the hypogenetic chaotic jerk system, the new system is established by DDDDttttqqqq0000 x = |y| − b y = (α + 3βw2)z z = |x| − y − az − w=z c (8). The Lyapunov exponent distribution is [+ 0 − −], so it is a chaotic system

Dynamical Analysis with the Order q

Dynamical Analysis with the Parameters

Dynamical Analysis with the Initial Values

Offset Boosting

Conclusions