Stability analysis and parameter classification of a reaction-diffusion model on an annulus

Sarfaraz, Wakil and Madzvamuse, Anotida (2019) Stability analysis and parameter classification of a reaction-diffusion model on an annulus. Journal of Applied Nonlinear Dynamics. ISSN 2164-6457 (Accepted)

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
School of Mathematical and Physical Sciences > Physics and Astronomy
Subjects: Q Science > QC Physics
Depositing User: Amelia Redman
Date Deposited: 15 Oct 2019 10:25
Last Modified: 05 Nov 2019 12:15
URI: http://sro.sussex.ac.uk/id/eprint/86862

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