Circuit Implementation Synchronization between Two Modified Fractional-Order Lorenz Chaotic Systems via a Linear Resistor and Fractional-Order Capacitor in Parallel Coupling

Juan Liu,Ping Zhou,Xuefeng Cheng,Viet-Thanh Pham

doi:10.1155/2021/6771261

Abstract

In this study, a modified fractional-order Lorenz chaotic system is proposed, and the chaotic attractors are obtained. Meanwhile, we construct one electronic circuit to realize the modified fractional-order Lorenz chaotic system. Most importantly, using a linear resistor and a fractional-order capacitor in parallel coupling, we suggested one chaos synchronization scheme for this modified fractional-order Lorenz chaotic system. The electronic circuit of chaos synchronization for modified fractional-order Lorenz chaotic has been given. The simulation results verify that synchronization scheme is viable.

Highlights

In the last twenty years, many fractional-order systems [1,2,3,4,5,6,7,8,9] have been used to discuss the dynamics, wave stability, initials, and boundary effect
Many real-world physical systems can be more accurately described by fractional-order differential equations (FODE) [3,4,5,6, 10, 11], e.g., diffusion-wave, super diffusion, heat conduction, dielectric polarization, viscoelasticity, and electromagnetic waves. e complex behavior such as chaos has been observed in many physical fractionalorder systems, e.g., the fractional-order brushless DC motor chaotic system [6], the fractional-order Lorenz chaotic system [7], the fractional-order Chua’s circuit [8], the fractional-order Duffing chaotic system [9], the fractional-order multistable locally active memristor [12], the fractional-order gyroscopes system [10], and the fractional-order microelectromechanical chaotic system [11]
Referring to synchronization between chaotic electronic circuits, the linear resistor coupling between two electronic circuits can realize the linear state variable coupling between chaotic systems, and the linear capacitive coupling or linear inductor coupling between two electronic circuits can realize the first derivative of state variable linear coupling

Summary

Introduction

In the last twenty years, many fractional-order systems [1,2,3,4,5,6,7,8,9] have been used to discuss the dynamics, wave stability, initials, and boundary effect. Based on the circuitry design method for fractionalorder nonlinear systems in [25,26,27,28,29], the circuit diagram to realize the fractional-order nonlinear chaotic system (4) is presented as Figure 3.

Coupling part

Maximum CLE

Conclusions