Analysis, Symmetry and Asymptotic Behaviour of Solutions for the Belousov-Zhabotinsky Model

Abstract

This research provides analytical insights in connection with the solutions of the Oregonator model, a refined iteration of the iconic Belousov-Zhabotinsky (BZ) reaction problem. This chemical process, initially observed by B. P. Belousov while replicating the Krebs cycle in vitro and later modified by Zhabotinsky using Fephenanthroline (ferroin), has become a hallmark example of nonlinear dynamics, chaos theory, and has parallels in various biological systems. Our study systematically delves into the boundedness, regularity, and possible symmetries of weak solutions. We explore traveling waves using the Tanh-method, alongside examining asymptotic solutions entrenched in self-similar forms and exponential scaling leading to a Hamilton-Jacobi equation. This research emphasizes on mathematical arguments along with the dynamics of the involved chemical concentrations. We provide new forms of analytical solutions showing them in a comprehensive manner that connects with the interpretation of the Oregonator model and its broader implications in chemical systems.