Murphy, Laura, Venkataraman, Chandrasekhar and Madzvamuse, Anotida (2018) Parameter identification through mode isolation for reaction-diffusion systems on arbitrary geometries. International Journal of Biomathematics, 11 (4). p. 1850053. ISSN 1793-5245
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Abstract
We present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many natural phenomena in areas such as developmental and cancer biology, cell motility and material science. In many of these applications, often one is interested in identifying parameters which will lead to a particular pattern for a given reaction-diffusion model. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of do- mains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that the inhomogeneous steady state can be a linear combination of eigenfunctions. Finally we show an example suggesting that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.
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: | 01 May 2018 13:02 |
Last Modified: | 26 Sep 2018 13:57 |
URI: | http://srodev.sussex.ac.uk/id/eprint/75568 |
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📧 Request an updateProject Name | Sussex Project Number | Funder | Funder Ref |
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Unravelling new mathematics for 3D cell migration | G1438 | LEVERHULME TRUST | RPG-2014-149 |
Mathematical Modelling and Analysis of Spatial Patterning on Evolving Surfaces | G0872 | EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL | EP/J016780/1 |