The effect of retardation in the random networks of excitable nodes, embeddable in the Euclidean space

Some features of random networks with excitable nodes that are embeddable in the Euclidean space are not describable in terms of the conventional integrate and fire model alone, and some further details should be involved. In the present paper we consider the effect of the retardation, i.e. the time that is needed for a signal to traverse between two agents. This effect becomes important to discover the differences between, e.g. the neural networks with low and fast axon conduct times. We show that the inclusion of the retardation effects makes some important changes to the statistical properties of the system. It considerably diminishes the amplitude of the possible oscillations in the random network. Additionally, it causes the critical exponents in the critical regime to considerably change.