Threshold setting and mean firing rates in networks of integrate-and-fire neurons


Hamish Meffin and William G. Gibson


Research Report 98-16
Date: 24 July 1998


The time-course and stability of the firing rates in a network of interconnected spiking integrate-and-fire neurons is analyzed for the simplified case where the conduction of the neuron's membrane is taken to be zero. The treatment is valid for networks of arbitrary size, no symmetry requirements are placed on the inter-neuronal connections and constant external inputs are allowed. An equation is given that explicitly relates the mean firing rates to the neuronal threshold, the synaptic response functions and the external inputs.

For purely excitatory networks the Perron-Frobenius theorem for non-negative matrices allows the existence and stability of the steady states to be related to the eigenvalues and eigenvectors of the matrix of synaptic connections.

The addition of inhibition allows more complex behaviour which is studied using a mixture of theory and computer simulations. In contrast to the excitatory case, the final state now depends on the initial state, thus allowing the possibility of memory storage. In addition, such a network can exhibit multistable and oscillatory behaviours.

Key phrases

neural network. integrate-and-fire neurons.

AMS Subject Classification (1991)

Primary: 92B20


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Sydney Mathematics and Statistics