Spiral Waves in Reaction-Diffusion Equations

We consider the reaction-diffusion system RT = ² R + R (1 - R² -), \\ R T = R ² + 2 R + qR³ \\ gathered system governs the solutions of reaction-diffusion systems near a Hopf bifurcation point. In two spatial dimensions we use formal asymptotic expansions to contruct one-armed and multi-armed Archimedean spiral waves for small values of the parameter q. We then show that the one-armed spiral waves are probably stable and the multi-armed ones are unstable for | q | small. Next, by numerical continuation methods, we construct spiral waves for all q. These calculations show that the one-armed spiral waves are unstable when | q | > 1. 397. We also find the explicit one-dimensional analogues of spiral waves for all q, and show that they are unstable for | q | small.