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

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