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Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion
journal contribution
posted on 2023-06-09, 13:18 authored by Anotida MadzvamuseAnotida Madzvamuse, Raquel BarreiraIn 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.
Funding
Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces; G0872; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/J016780/1
New predictive mathematical and computational models in experimental sciences; G1949; ROYAL SOCIETY; WM160017
Unravelling new mathematics for 3D cell migration; G1438; LEVERHULME TRUST; RPG-2014-149
InCeM: Research Training Network on Integrated Component Cycling in Epithelial Cell Motility; G1546; EUROPEAN UNION; 642866 - InCeM
Coupling Geometric PDEs with Physics; ISAAC NEWTON INSTITUTE FOR MATHEMATICAL SCIENCES; EP/K032208/1
History
Publication status
- Published
File Version
- Accepted version
Journal
Discrete and Continuous Dynamical Systems - Series BISSN
1531-3492Publisher
American Institute of Mathematical SciencesExternal DOI
Issue
7Volume
23Page range
2775-2801Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2018-05-16First Open Access (FOA) Date
2019-06-01First Compliant Deposit (FCD) Date
2018-05-15Usage metrics
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