Abstract.
If in the classical Turing model the diffusion process (Brownian motion) is replaced by a more general correlated random walk, then the parameters describing spatial spread are the particle speeds and the rates of change in direction. As in the Turing model, a spatially constant equilibrium can become unstable if the different species have different turning rates and different speeds. Furthermore, a Hopf bifurcation can be found if the reproduction rate of the activator is greater than its rate of change of direction, and oscillating patterns are possible.
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Received 24 February 1995; received in revised form 6 September 1995
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Hillen, T. A Turing model with correlated random walk. J Math Biol 35, 49–72 (1996). https://doi.org/10.1007/s002850050042
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DOI: https://doi.org/10.1007/s002850050042