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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Numerical Analysis Seminars: Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

Presented by Dr. Anotida Madzvamuse, University of Sussex

25 February 2011 13:15 in CG218

By using asymptotic theory, I generalise the Turing diffusively-driven
instability conditions for reaction-diffusion systems with slow, isotropic
domain growth. In this talk, I will show that 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. These theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular I will 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.

Contact David.Bourne@durham.ac.uk for more information