Self-organized criticality of a simple integrate-and-fire neural model

We consider a simple integrate-and-fire neural model without synaptic plasticity. In this model, the membrane potential propagates to the nearest neighbor neurons when that potential is greater than a threshold value. When a neuron is fired, the propagating potential is leaky. Therefore, the sum of the received potential is less than the presynaptic potential. We simulated this simple model on a fully-connected network. We identified the critical membrane strength, J c = 4.71(1). At the critical membrane strength, we observed that the probability distribution function of the avalanche shows a power law, P(s) ≈ s −τ, with the critical exponent τ = 1.414(5). The lifetime of the avalanche also showed a power law. The power law behaviors imply that this model shows self-organized criticality.