Abstract：
:Reactivity (a.k.a initial growth) is necessary for diffusion driven instability (Turing instability). Using a notion of common Lyapunov function we show that this necessary condition is a special case of a more powerful (i.e. tighter) necessary condition. Specifically, we show that if the linearised reaction matrix and the diffusion matrix share a common Lyapunov function, then Turing instability is not possible. The existence of common Lyapunov functions is readily checked using semi-definite programming. We apply this result to the Gierer-Meinhardt system modelling regenerative properties of Hydra, the Oregonator, to a host-parasite-hyperparasite system with diffusion and to a reaction-diffusion-chemotaxis model for a multi-species host-parasitoid community.
journal_name
Math Bioscijournal_title
Mathematical biosciencesauthors
Elragig A,Townley Sdoi
10.1016/j.mbs.2012.04.006subject
Has Abstractpub_date
2012-09-01 00:00:00pages
131-8issue
1eissn
0025-5564issn
1879-3134pii
S0025-5564(12)00093-4journal_volume
239pub_type
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