Robustness of spiral waves in two-dimensional reactive–diffusive media

Abstract

The effects of the reaction terms, diffusion coefficients and size of the computational domain on the dynamics of the two-equation Oregonator model in two-dimensional reactive–diffusive media is studied numerically, and it is shown that spiral waves are robust under truncation or expansion of the computational domain. It is also shown that large diffusion coefficients for the inhibitor may result on either annihilation of the wave or unbounded growth, whereas large diffusion coefficients for the activator concentration may result in unbounded decay of both the activator’s and inhibitor’s concentrations. Small diffusion coefficients of the inhibitor may result in stationary tongue-like shapes, whereas small diffusion coefficients of the activator may result in narrow ring shapes where the activator’s concentration is high. A decrease in the parameter which controls the stiffness of the activator’s reaction rate is found to result in unbounded growth of the activator’s concentration, whereas an increase in the parameter that couples the activator and inhibitor is found to result in either annihilation of the spiral wave or unbounded growth of the concentrations of both the activator and the inhibitor.