On bifurcations of spiral waves in the plane

E.V. Nikolaev, V.N. Biktashev, A.V. Holden

Submitted to IJBC 1999/01/19. Accepted 1999/01/30.

We describe the simplest bifurcations of spiral waves in reaction-diffusion systems in the plane and present the list of model systems. One-parameter bifurcations of one-armed spiral waves are fold and Hopf bifurcations. Multi-armed spiral waves may additionally undergo a period-doubling pitchfork bifurcation, when two congruent spiral wave solutions, having the `double' period, branch from the original spiral wave at the bifurcation point.