Drift of spiral waves on nonuniformly curved surfaces

The evolution of spiral waves on nonuniformly curved surfaces is theoretica lly investigated in the framework of kinematic approach. We predict the exi stence of the drift proportional to the gradient of Gaussian. curvature of the surface. In the excitable media with equal diffusion coefficients of ac tivator and inhibitor the direction of the drift is perpendicular to the gr adient of Gaussian curvature. If the diffusion coefficients are different t he component of the velocity drift parallel to the gradient of Gaussian cur vature appears. In the particular case of the paraboloid of revolution the spiral wave will "climb up" onto the top of the paraboloid. This theoretica l prediction is confirmed by computer simulations. The drift of spiral wave s towards the top of parabolic surface was observed in experiments with BZ reaction. The experimental results are also presented.