Geometric theory of trigger waves ? A dynamical system approach

Abstract

We propose a geometric model for wave propagation in excitable media. Our model is based on the Fermat principle and it resembles that of Wiener and Rosenblueth. The model applies to the propagation of excitations, such as chemical and biological wave fronts, grass fire, etc. Starting from the Fermat principle, some consequences of the assumptions are derived analytically. It is proved that the model describes a dynamical system, and that the wave propagates along “ignition lines” (extremals). The theory is applied to the special cases of tube reactor and annular reactor. The asymptotic shape of the wave fronts is derived for these cases: they are straight lines perpendicular to the tube, and involutes of the central obstacle, respectively.