Dual Lyapunov-based Synchronization Control of Rössler System

Abstract

This paper proposes a novel approach for the synchronization problem of nonlinear dynamical systems, integrating dual Lyapunov stability analysis with polynomial optimization. A comprehensive review of the relevant scientific literature on synchronization methods is conducted, with a particular focus on classical Lyapunov-based methods for chaotic systems. In this study, the Rössler system is synchronized by employing dual Lyapunov-based closed-loop synchronization method. This method uses semidefinite programming and sum-of-squares polynomials to compute a nonlinear state feedback function which synchronize a chaotic system to a selected reference model. It is aimed that chaotic behavior is destroyed and, instead, a limit cycle becomes attracting. Simulation works are performed for randomly selected 100 different initial conditions to show that synchronization process is successfully performed. Furthermore, bifurcation diagrams and phase portraits are evaluated to analyze the system dynamics. The paper discusses results and how new constraints should be employed and adapted to more complex systems.

Presented at the International Interdisciplinary Chaos Symposium on Chaos and Complex Systems (SCCS 2025), Istanbul, Türkiye. A version of this work has been accepted for publication in the conference proceedings and will appear in Chaos and Complex Systems: Proceedings of the 6th International Interdisciplinary Chaos Symposium (Springer Cham)