Stability Analysis and Parameter Classification of a Reaction-Diffusion Model on an Annulus - Sarfaraz, Wakil; Madzvamuse, Anotida (Journal of Applied Nonlinear Dynamics, 2026)
This work explores the influence of domain-size on the evolution of pattern formation modelled by an activator-depleted reaction-diffusion system on a flat-ring (annulus). A closed form expression is derived for the spectrum of the Laplace operator on the domain. Spectral method is used to depict the close form solution on the domain. The bifurcation analysis of activator-depleted reaction-diffusion system is conducted on the admissible parameter space under the influence of domain-size. The admissible parameter space is partitioned under a set of proposed conditions relating the reaction-diffusion constants with the domain-size. Finally, the full system is numerically simulated on a two dimensional annular region using the standard Galerkin finite element method to verify the influence of the analytically derived domain-dependent conditions.