Persistent Activity in Assortative Networks of Integrate and Fire Neurons

A neuronal network can be represented as a directed graph. Each neuron corresponds to a node and each connection between the axon of one neuron and the dendrite of another corresponds to an edge. We investigate the effects of two statistical properties of directed graphs on the capacity of excitatory and inhibitory neuronal networks to exhibit bistability. One measure is node-degree correlation, the propensity of nodes to have similar in-degrees and out-degrees. The other measure is edge-degree correlation, the correlation between the in-degree of one node and the out-degree of a node receiving input from the first. By grouping subpopulations of neurons according to their in and out degrees, we perform simulations testing the effect of these different forms of assortativity on network input/output properties. We show that the node-degree correlation and edge-degree correlation of a neuronal network affect the ranges of synaptic coupling strengths and of external stimulation rates for which there are two steady-state mean firing rates. The existence of bistability and hysteresis is important as the physiological basis of short term memory