TY - JOUR
T1 - Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
AU - Madzvamuse, Anotida
AU - Gaffney, Eamonn A.
AU - Maini, Philip K.
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: AM would like to acknowledge Professors Georg Hetzer and Wenxian Shen (Auburn University, USA) for fruitful discussions. EAG: This publication is based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). PKM was partially supported by a Royal Society Wolfson Merit Award.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2009/8/29
Y1 - 2009/8/29
N2 - 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. © Springer-Verlag 2009.
AB - 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. © Springer-Verlag 2009.
UR - http://hdl.handle.net/10754/599707
UR - http://link.springer.com/10.1007/s00285-009-0293-4
UR - http://www.scopus.com/inward/record.url?scp=77952289005&partnerID=8YFLogxK
U2 - 10.1007/s00285-009-0293-4
DO - 10.1007/s00285-009-0293-4
M3 - Article
C2 - 19727733
SN - 0303-6812
VL - 61
SP - 133
EP - 164
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
IS - 1
ER -