AUTHOR=Tarammim Absana , Akter Musammet Tahmina 

TITLE=Shimizu–Morioka's chaos synchronization: An efficacy analysis of active control and backstepping methods

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 9 - 2023

YEAR=2023

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2023.1100147

DOI=10.3389/fams.2023.1100147

ISSN=2297-4687

ABSTRACT=This research inspects the effectiveness of synchronization methods Active control and Backstepping control from systematic design procedures of synchronized  Shimizu-Morioka system for the same parameter. To achieve synchronization between the state variables of two identical Shimizu-Morioka chaotic systems by defining the proposed varieties of the error dynamics coefficient matrix, we design an active controller that enables the synchronization of these systems. We prove the stability of the synchronization of the nonlinear identical Shimizu-Morioka system using the designed recursive backstepping nonlinear controllers basis on the Lyapunov function. The new virtual state variable and establishing Lyapunov functionals are used in the backstepping controller to stabilize and reduce errors between the Master(MS)/ Drive(DS) systems. For comparison, the complexity of active controllers is verified that the designed controller's effectiveness based on Backstepping is attainable in engineering applications. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed synchronization strategy with the Runge-Kutta(RK-4) algorithm of 4th order through the MatLab Simulink.