Pattern formation in excitable media with concentration-dependent diffusivities.
We study a model of pattern formation in an excitable medium with concentration-dependent diffusivities. The reaction terms correspond to a two-variable Gray-Scott model in which the system has only one stable steady state. The diffusion coefficients of the two species are assumed to have a functional relationship with the concentration of the autocatalyst. A transition from self-replicating behavior to stationary spots is observed as the influence of the local autocatalyst concentration on the diffusion process increases. Notably, the transition occurs even though there is no change in the relative diffusivities of the activator and inhibitor. The observed time-independent patterns exhibit an unusual dependence on the size and geometry of an initial perturbation. Initial perturbations with a large spatial size, for example, sometimes revert to the homogeneous equilibrium state, whereas perturbations of smaller spatial extent develop into stable spots at the same parameter values.