Finite-Time Synchronization of the Rabinovich and Rabinovich-Fabrikant Chaotic Systems for Different Evolvable Parameters

Edwin A. Umoh (Department of Electrical and Electronic Engineering Technology, Federal Polytechnic, Kaura Namoda)
Alfian Ma'arif (Department of Electrical Engineering, Universitas Ahmad Dahlan, Yogyakarta)
Omokhafe J. Tola (Department of Electrical and Electronic Engineering, Federal University of Technology, Minna)
Iswanto Suwarno (Department of Electrical Engineering, Universitas Muhammadiyah Yogyakarta, Yogyakarta)
Muhammed N. Umar (Department of Electrical and Electronic Engineering Technology, Federal Polytechnic, Kaura Namoda)

International Journal of Robotics and Control Systems
Vol 3, No 4 (2023)

This paper addresses the challenge of synchronizing the dynamics of two distinct 3D chaotic systems, specifically the Rabinovich and Rabinovich-Fabrikant systems, employing a finite-time synchronization approach. These chaotic systems exhibit diverse characteristics and evolving chaotic attractors, influenced by specific parameters and initial conditions. Our proposed low-cost finite-time synchronization method leverages the signum function's tracking properties to facilitate controlled coupling within a finite time frame. The design of finite-time control laws is rooted in Lyapunov stability criteria and lemmas. Numerical experiments conducted within the MATLAB simulation environment demonstrate the successful asymptotic synchronization of the master and slave systems within finite time. To assess the global robustness of our control scheme, we applied it across various system parameters and initial conditions. Remarkably, our results reveal consistent synchronization times and dynamics across these different scenarios. In summary, this study presents a finite-time synchronization solution for non-identical 3D chaotic systems, showcasing the potential for robust and reliable synchronization under varying conditions.