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Pattern formation in the bistable Gray-Scott model

Author

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

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.

Suggested Citation

  • Mazin, W. & Rasmussen, K.E. & Mosekilde, E. & Borckmans, P. & Dewel, G., 1996. "Pattern formation in the bistable Gray-Scott model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 40(3), pages 371-396.
    • Handle: RePEc:eee:matcom:v:40:y:1996:i:3:p:371-396
    DOI: 10.1016/0378-4754(95)00044-5
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    Cited by:

    1. Ishtiaq Ali & Maliha Tehseen Saleem, 2023. "Spatiotemporal Dynamics of Reaction–Diffusion System and Its Application to Turing Pattern Formation in a Gray–Scott Model," Mathematics, MDPI, vol. 11(6), pages 1-17, March.

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    Keywords

    Reaction; Diffusion; Bifurcation;
    All these keywords.

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