BIFURCATION TO SPIRAL WAVES IN REACTION-DIFFUSION SYSTEMS

For a large class of reaction-diffusion systems on the plane, we show rigorously that m-armed spiral waves bifurcate from a homogeneous equi librium when the latter undergoes a Hopf bifurcation. In particular, w e construct a finite-dimensional manifold which contains the set of sm all rotating waves close to the homogeneous equilibrium. Examining the flow on this center-manifold in a very general example, we find diffe rent types of spiral waves, distinguished by their speed of rotation a nd their asymptotic shape at large distances of the tip. The relation to the special class of lambda-omega systems and the validity of these systems as an approximation is discussed.