A novel significant parameter in the dynamics of periodic waves in excitable media

Wave selection in excitable media is an important problem of nonlinear dynamics. Same aspects of this problem have been solved already in application to a propagation of a solitary wave. In this talk a periodic sequence of wave segments is analysed. By direct numerical simulations performed on the modified FitzHugh-Nagumo model and by application of a free-boundary approach it is shown that such sequence can be stabilized only in a restricted domain within the parameter space. An introduced parameter predetermines the propagation velocity and the shape of the wave segments and reaches a constant critical value at the whole boundary of the existence domain. Moreover, another constant value of this novel parameter corresponds to zero tension of a scroll wave filament in a 3D medium.