Link to bioRxiv paper:

http://biorxiv.org/cgi/content/short/2020.11.09.374934v1?rss=1

Authors: Haas, P. A., Goldstein, R. E.

Abstract:

Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in generic systems with N=2 diffusing species, forcing experimental realizations of the instability to rely on fluctuations or additional non-diffusing species. Here we ask whether this diffusive threshold lowers for N>2 to allow "true" Turing instabilities. Inspired by May's analysis of the stability of random ecological communities, we analyze the threshold for reaction-diffusion systems whose linearized dynamics near a homogeneous fixed point are given by a random matrix. In the numerically tractable cases of N[≤]6, we find that the diffusive threshold generically decreases as N increases and that these many-species instabilities generally require all species to be diffusing.

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