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 |
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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: | 22 Aug 2018 13:38 |
URI: | http://srodev.sussex.ac.uk/id/eprint/75868 |
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📧 Request an updateProject Name | Sussex Project Number | Funder | Funder Ref |
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Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces | G0872 | EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL | EP/J016780/1 |
Coupling Geometric PDEs with Physics | Unset | ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES | EP/K032208/1 |