期刊
JOURNAL OF MATHEMATICAL BIOLOGY
卷 61, 期 1, 页码 133-164出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00285-009-0293-4
关键词
Convection-reaction-diffusion systems; Turing diffusively-driven instability; Pattern formation; Growing domains asymptotic theory; Domain-induced diffusively-driven instability
资金
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-04]
- Royal Society Wolfson Merit
- EPSRC [EP/H020349/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/H020349/1] Funding Source: researchfish
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.
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