Oscillatory wave patterns and spiral breakup in the Brusselator model using numerical bifurcation analysis

This article addresses the core breakup analysis of the spiral dynamics of an oscillatory system of chemical reactions, the so-called Brusselator model. We first obtain stable oscillatory periodic solutions corresponding to the stable limit cycle near a Hopf bifurcation point when the diffusion terms are neglected. Then, we investigate the occurrence of periodic traveling wave solutions of the model and perform the stability analysis of these solutions on the parameter plane. A stability boundary is also identified on the parameter plane. In the two-dimensional spatial domain, we illustrate rotating spiral waves and their instability that leads to a spiral breakup from the center of rotation.

Automated summary

This article explores the stable oscillatory periodic solutions and periodic traveling wave solutions of the Brusselator model, as well as stability analysis and stability boundary on the parameter plane. It also demonstrates rotating spiral waves and their instability in the two-dimensional spatial domain.