Noise-sustained oscillation and synchronization of excitable media with stirring

Constructive effects of noise have been well studied in spatially extended systems. In most of these studies, the media are static, reaction-diffusion type, and the constructive effects are a consequence of the interplay between local excitation due to noise perturbation and propagation of excitation due to diffusion. Many chemical or biological processes occur in a fluid environment with mixing. In this paper, we investigate the interplay among noise, excitability, diffusion and mixing in excitable media advected by a chaotic flow, in a 2D Fitz Hugh-Nagumo model described by a set of reaction-advection- diffusion equations. Without stirring, noise can only generate non-coherent excited patches of the static media. In the presence of stirring, we observe three dynamical and pattern formation regimes: i.) Non-coherent excitation, when mixing is not strong enough to achieve synchronization of independent excitations developed at different locations; ii.) Coherent global excitation, when the noise-induced perturbation propagates by mixing and generates a synchronized excitation of the whole domain; and iii.) Homogenization, when strong stirring dilutes quickly those noise-induced local excitations. In the presence of an external sub-threshold periodic forcing, the period of the noise-sustained oscillations can be locked by the forcing period with different ratios. Our results may be verified in experiments and find applications in population dynamics of oceanic ecological systems.