A set of travelling fronts of excitation in the model of homogeneous neuro-like medium with nonlocal coupling

The influence of arbitrary nonlocal coupling on the existence and properties of autowave processes in a bistable medium is investigated. Approximation of the individual activity function F(x) by a Heaviside unit function allows one to obtain some analytical results. The calculations clearly testify to the relation between the instability of the plane front of excitation, observed by A.V. Masterov et al. (1988), and nonlocal inhibition of the space-coupling function; they provide mathematical means for determining the characteristic scale of structures emerging in the process of front deterioration. If an ordinary traveling front is unsteady in a two-dimensional medium, the whole set of fronts under study is unsteady. Therefore, a quasi-independent description of wave processes in the longitudinal and transverse directions is possible for a neuro-like medium