On the stability of the willamowsky-Rossler chaotic reaction diffusion model

Abstract

The study of dynamical systems is a fundamental topic in the natural and engineering sciences, contributing to understanding the behavior of complex systems and analyzing their stability. In this study, we will analyze a dynamical system containing six equilibria, with the aim of classifying the system's parameter regions based on the presence of these equilibria and determining their stability conditions. We will use the Lyapunov method to analyze local and global stability, and evaluate the presence of a Hopf bifurcation at a particular equilibrium point in the Wilamowski-Rössler system. In addition, we will

discuss the study of interaction propagation in three- dimensional systems and global asymptotic stability in

the partial differential equations (PDEs) representing these systems. This study aims to achieve a deeper understanding of the system's dynamics and determine the stability conditions of its equilibria, contributing to the development of knowledge in the field of dynamical systems and their applications.