WAVE-SPLITTING IN THE BISTABLE GRAY-SCOTT MODEL

Abstract

The Gray-Scott model describes a chemical reaction in which an activator species grows autocatalytically on a continuously fed substrate. For certain feed rates and activator life times the model allows for the coexistence of two different homogeneous steady states, the red state in which the conditions correspond to those of the pure substrate, and the blue state where the activator concentration is relatively high and limited by substrate depletion. The blue state may again undergo a Hopf bifurcation leading to self-sustained oscillations and, for a spatially extended system, this state may also exhibit a subcritical Turing bifurcation capable of producing global as well as localized, stationary spatial structures. Interactions between these instabilities can lead to a variety of different phenomena including Turing-Hopf mixed modes and spatio-temporal chaos. The paper presents the results of a computer simulation study of some of these far-from-equilibrium phenomena. Special emphasis is given to the propagation, collision and splitting of the traveling pulses which can develop in response, for instance, to strong local perturbations of the red state in a region of parameter space where the blue state is Turing and Hopf unstable.