Steady State of an Inhibitory Neural Network

Details Steady State of an Inhibitory Neural Network Steady State of an Inhibitory Neural Network

2001-05-24

arxiv.org/abs/nlin/0105058v1

Phys. Rev. E 64, 041906 (2001)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

6 pages, 4 figures, 2-column format, to be submitted to PRE

Scientific paper

10.1103/PhysRevE.64.041906

We investigate the dynamics of a neural network where each neuron evolves according to the combined effects of deterministic integrate-and-fire dynamics and purely inhibitory coupling with K randomly-chosen "neighbors". The inhibition reduces the voltage of a given neuron by an amount Delta when one of its neighbors fires. The interplay between the integration and inhibition leads to a steady state which is determined by solving the rate equations for the neuronal voltage distribution. We also study the evolution of a single neuron and find that the mean lifetime between firing events equals 1+K*Delta and that the probability that a neuron has not yet fired decays exponentially with time.

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