Self-organized criticality of a simplified integrate-and-fire neural model on random and small-world network

TL;DR

This paper investigates the self-organized criticality of a simplified integrate-and-fire neural model across different network topologies, revealing universal critical behavior in small-world and random networks but not in regular networks.

Contribution

The study simplifies the LHG model and demonstrates that small-world and random networks exhibit the same critical exponents, highlighting the role of shortcuts in criticality.

Findings

Power law distributions observed for avalanche size and lifetime.

Critical exponents are consistent in small-world and random networks.

Regular networks do not exhibit critical behavior.

Abstract

We consider the criticality for firing structures of a simplified integrate-and-fire neural model on the regular network, small-world network, and random networks. We simplify an integrate-and-fire model suggested by Levina, Herrmann and Geisel (LHG). In our model we set up the synaptic strength as a constant value. We observed the power law behaviors of the probability distribution of the avalanche size and the life time of the avalanche. The critical exponents in the small-world network and the random network were the same as those in the fully connected network. However, in the regular one-dimensional ring, the model does not show the critical behaviors. In the simplified LHG model, the short-cuts are crucial role in the self-organized criticality. The simplified LHG model in three types of networks such as the fully connected network, the small-world network, and random network belong to the same universality class.