Pattern formation in the bistable Gray-Scott model

W. Mazin, K.E. Rasmussen, E. Mosekilde, P. Borckmans and G. Dewel

Mathematics and Computers in Simulation (MATCOM), 1996, vol. 40, issue 3, 371-396

Abstract: This paper presents a computer simulation study of a variety of far-from-equilibrium phenomena that can arise in a bistable chemical reaction-diffusion system which also displays Turing and Hopf instabilities. The Turing bifurcation curve and the wave number for the patterns of maximum linear growth rate are obtained from a linear stability analysis. The distribution in parameter space of a wide variety of different spatio-temporal attractors that can be reached through a strong, local perturbation of the linearly stable homogeneous steady state is mapped out. These include global Turing structures, stable localized structures, interacting fronts, mixed Turing-Hopf modes, and spatio-temporal chaos. Special emphasis is given to the newly discovered spot multiplication process in which cell-like structures replicate themselves until they occupy the entire system. We also present results on the formation of lace-like patterns.

Keywords: Reaction; Diffusion; Bifurcation (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:40:y:1996:i:3:p:371-396

DOI: 10.1016/0378-4754(95)00044-5

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