Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion

Madzvamuse, Anotida and Barreira, Raquel (2018) Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion. Discrete and Continuous Dynamical Systems - Series B, 23 (7). pp. 2775-2801. ISSN 1531-3492

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Abstract

In this article we present, for the first time, domain-growth induced pat- tern formation for reaction-diffusion systems with linear cross-diffusion on evolving domains and surfaces. Our major contribution is that by selecting parameter values from spaces induced by domain and surface evolution, patterns emerge only when domain growth is present. Such patterns do not exist in the absence of domain and surface evolution. In order to compute these domain-induced parameter spaces, linear stability theory is employed to establish the necessary conditions for domain- growth induced cross-diffusion-driven instability for reaction-diffusion systems with linear cross-diffusion. Model reaction-kinetic parameter values are then identified from parameter spaces induced by domain-growth only; these exist outside the classical standard Turing space on stationary domains and surfaces. To exhibit these patterns we employ the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 16 May 2018 14:27
Last Modified: 01 Jun 2019 01:00
URI: http://sro.sussex.ac.uk/id/eprint/75868

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Project NameSussex Project NumberFunderFunder Ref
Unravelling new mathematics for 3D cell migrationG1438LEVERHULME TRUSTRPG-2014-149
Mathematical Modelling and Analysis of Spatial Patterning on Evolving SurfacesG0872EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCILEP/J016780/1
Coupling Geometric PDEs with PhysicsUnsetISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCESEP/K032208/1