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

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posted on 2023-06-09, 19:16 authored by Wakil Sarfaraz, Anotida MadzvamuseAnotida Madzvamuse
This work explores the influence of domain-size on the evolution of pattern formation modelled by an activator-depleted reactiondiffusion 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 reactiondiffusion 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 reactiondiffusion 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.

Funding

InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION

New predictive mathematical and computational models in experimental sciences; G1949; ROYAL SOCIETY; WM160017

Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Journal of Applied Nonlinear Dynamics

ISSN

2164-6457

Publisher

L&H Scientific Publishing

Issue

4

Volume

9

Page range

589-617

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2019-10-15

First Open Access (FOA) Date

2019-10-18

First Compliant Deposit (FCD) Date

2019-10-14

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