Abstract
The problem of pattern formation in a generic two species reaction–diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by working in the generalized setting of a stochastic formulation to the inspected problem, spatially organized patterns can develop, seeded by finite size corrections. General conditions are given for the stochastic patterns to occur. The predictions of the theory are tested for a specific case study.
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Notes
The fact a discretised domain can produce wave modes that do not exist in the continuum case was also noticed in Woolley et al. (2011).
For the sake of simplicity, and without loosing generality we will set \(a=1\) in the following.
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Cantini, L., Cianci, C., Fanelli, D. et al. Stochastic amplification of spatial modes in a system with one diffusing species. J. Math. Biol. 69, 1585–1608 (2014). https://doi.org/10.1007/s00285-013-0743-x
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DOI: https://doi.org/10.1007/s00285-013-0743-x