Neural networks with transient state dynamics

We investigate dynamical systems characterized by a time series of distinct semi-stable activity patterns, as they are observed in cortical neural activity patterns. We propose and discuss a general mechanism allowing for an adiabatic continuation between attractor networks and a specific adjoined transient-state network, which is strictly dissipative. Dynamical systems with transient states retain functionality when their working point is autoregulated avoiding prolonged periods of stasis or drifting into a regime of rapid fluctuations. We show, within a continuoustime neural network model, that a single local updating rule for online learning allows simultaneously (a) for information storage via unsupervised Hebbian-type learning (b) for adaptive regulation of the working point and (c) for the suppression of runaway synaptic growth. Simulation results are presented, the spontaneous breaking of timereversal symmetry and link symmetry are discussed. Transient state dynamics 2