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

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.