Transition from self-replicating behavior to stationary patterns induced by concentration-dependent diffusivities

Abstract

In this Letter, we report the observation of a transition from self-replicating behavior to stationary spatial structures induced by concentration-dependent diffusivities in the excitable Gray-Scott medium. Notably, the transition occurs even though there is no change in the relative diffusivities between the activator and the inhibitor. In contrast to the well-known Turing patterns, the obtained time-independent spatial structure has no intrinsic wavelength and the asymptotic state depends exclusively on the initial perturbations. This study illustrates that variable diffusivities can also have profound effects on pattern formation and selection in excitable media.