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

摘要

) by aHeaviside unit function allows one to obtain some analytical results.The calculations clearly testify to the relation between the instabilityof the plane front of excitation, observed by A.V. Masterov et al.(1988), and nonlocal inhibition of the space-coupling function; theyprovide mathematical means for determining the characteristic scale ofstructures emerging in the process of front deterioration. If anordinary traveling front is unsteady in a two-dimensional medium, thewhole set of fronts under study is unsteady. Therefore, aquasi-independent description of wave processes in the longitudinal andtransverse directions is possible for a neuro-like medium