Spatiotemporal patterns in the Bär model induced by concentration-dependent diffusivities

Abstract

We investigate the effects of diffusivity on pattern formation in the excitable 2D Bär model with periodic boundary conditions. Our work generalizes previous findings of Roussel and coworkers in 1D and focusses on the turbulent states, including the spiral breakdown process. Diffusion coefficients (D(u)) quadratically dependent on the activator concentration were studied. Inhibition of the spiral instability was found with a negative linear coefficient in the concentration dependence of D(u). At a given value of e the inhibition can be complete for nonflux boundary conditions while a delay of the instability occurs in systems with periodic boundary conditions. Positive quadratic coefficients in the concentration dependence of D(u) strongly modify the defect statistic in the chaotic zone.