Tools
Tools
Madzvamuse, Anotida, Gaffney, Eamonn A and Maini, Philip K (2010) Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains. Journal of Mathematical Biology, 61 (1). pp. 133-164. ISSN 0303-6812
Full text not available from this repository.Abstract
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth.
| Item Type: | Article |
|---|---|
| Additional Information: | My contribution to this paper was around 85% |
| Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
| Depositing User: | Anotida Madzvamuse |
| Date Deposited: | 06 Feb 2012 18:11 |
| Last Modified: | 01 Nov 2012 17:13 |
| URI: | http://sro.sussex.ac.uk/id/eprint/15121 |