title: Stability of fully asynchronous discrete-time discrete-state dynamic networks.
abstract: We consider networks of a large number of neurons (or units, processors, ...), whose dynamics are fully asynchronous with overlapping updating. We suppose that the neurons take a finite number of states (discrete states), and that the updating scheme is discrete in time. We make no hypotheses on the activation function of the neurons; the networks may have multiple cycles and basins. We derive conditions on the initialization of the networks, which ensures convergence to fixed points only. Application to a fully asynchronous Hopfield neural network allows us to validate our study.
authors.affiliation: LIFC, IUT de Belfort-Montbeliard, Belfort, France.
authors.forename: J M
authors.initials: JM
authors.lastname: Bahi
authors.forename: S
authors.initials: S
authors.lastname: Contassot-Vivier