Coexistence of Multiple Attractors in a Novel Simple Jerk Chaotic Circuit With CFOAs Implementation

Qiao Wang,Xianming Wu,Zean Tian,Weijie Tan

doi:10.3389/fphy.2022.835188

Abstract

A novel, simple Jerk chaotic circuit with three current feedback operational amplifiers included (CFOA-JCC) is proposed, which has a simpler circuit structure, fewer components, but higher frequency characteristics. The dynamic behaviors of CFOA-JCC are analyzed, including equilibrium, stability, Lyapunov exponent, bifurcation diagram, offset boosting, and phase diagram. Furthermore, the frequency spectrum characteristic of the ordinary op-amps Jerk chaotic circuit was compared with CFOA-JCC under the same circuit parameters, and the chaotic attractor frequency of CFOA-JCC can reach about 650 kHz, much better than that of ordinary op-amps (12 kHz). Numerical simulation shows that CFOA-JCC has coexisting attractors, verified by hardware circuit experiments.

Highlights

Chaos is a complex nonlinear phenomenon with special dynamical properties, and various chaotic systems are found and widely used in the fields of electronic communication systems, control systems, and so on [1,2,3,4,5,6]
When C = 1 nF, the circuit with voltage feedback operational amplifiers (VFOA) is no longer chaotic. It can be seen from the frequency spectrum and the phase diagram that it is in a periodic state
The bifurcation analysis suggests that chaos that arises in the current feedback operational amplifier (CFOA)-JCC follows the classical period-doubling when adjusting the bifurcation control parameters slowly

Summary

INTRODUCTION

Chaos is a complex nonlinear phenomenon with special dynamical properties, and various chaotic systems are found and widely used in the fields of electronic communication systems, control systems, and so on [1,2,3,4,5,6]. In 2011, Sprott proposed a Jerk chaotic circuit with traditional voltage feedback operational amplifiers (VFOA). He did not discuss the coexistence of attractors of his system, and the circuit was not the simplest one. It illustrates the importance of the feedback resistance Rf of the CFOA, so Rf can be used to adjust the frequency response of the amplifier [31] This designed circuit configuration is shown, which includes three CFOAs; three capacitors C1, C2, C3; four resistors R1, R2, R3, R4, and a silicon diode named D1. The differential equations of the proposed system can be written as

R1C3 u3

CONCLUSION