title: Steady state of an inhibitory neural network.
abstract: 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 that 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.
authors.affiliation: Department of Physics, Boston University, Boston, MA, 02215, USA.
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky
authors.forename: S
authors.initials: S
authors.lastname: Redner
mesh_terms: D000465:Algorithms; D055592:Biophysical Phenomena; D001703:Biophysics; D006801:Humans; D008953:Models, Anatomic; D009415:Nerve Net; D009474:Neurons / Q000473:pathology*; D013816:Thermodynamics