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

TL;DR

This paper investigates how signal transmission delays, or retardation, in Euclidean space-embedded random networks of excitable nodes influence their dynamics, revealing suppression of oscillations and changes in critical behavior.

Contribution

It introduces the effect of retardation into the model, showing its impact on the statistical properties and critical exponents of the network dynamics.

Findings

Retardation suppresses amplitude of oscillations.

It significantly alters critical exponents.

Changes are notable compared to models without retardation.

Abstract

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 (IFM) 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 in the statistical properties of the system. It considerably suppresses/restricts the amplitude of the possible oscillations in the random network. Additionally, it causes the critical exponents in the critical regime to considerably change.