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Stability analysis of non-autonomous reaction-diffusion systems: The effects of growing domains

journal contribution
posted on 2023-06-07, 19:09 authored by Anotida MadzvamuseAnotida Madzvamuse, Eamonn A Gaffney, Philip K Maini
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.

History

Publication status

  • Published

Journal

Journal of Mathematical Biology

ISSN

0303-6812

Publisher

Springer

Issue

1

Volume

61

Page range

133-164

Department affiliated with

  • Mathematics Publications

Notes

My contribution to this paper was around 85%

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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