Critical properties of autowaves propagating on deformed cylindrical surfaces

Abstract

Propagation of ring-shaped autowaves on deformed cylindrical surfaces is studied theoretically within a kinematical model. Theoretical results predict the existence of a critical deformation of the surface above which propagation of ring-shaped fronts is impossible and the structure of stable autowaves becomes similar to the so-called V-patterns with free ends. This prediction is confirmed by numerical simulations of a two-variable reaction–diffusion excitable medium on a torus.