Pattern formation in the bistable Gray-Scott model

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.