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Some features of random networks with excitable nodes that are embeddable inthe Euclidean space are not describable in terms of the conventional integrateand fire model (IFM) alone, and some further details should be involved. In thepresent paper we consider the effect of the retardation, i.e. the time that isneeded for a signal to traverse between two agents. This effect becomesimportant to discover the differences between e.g. the neural networks with lowand fast axon conduct times. We show that the inclusion of the retardationeffects makes some important changes in the statistical properties of thesystem. It considerably suppresses/restricts the amplitude of the possibleoscillations in the random network. Additionally, it causes the criticalexponents in the critical regime to considerably change.

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