Dynamics of Activity in Biology-Oriented Neural Network Models: Stability at Low Firing Rates

We investigated the dynamics of activity in feedback neural network models at low firing rates. The networks were designed to capture the typical features of real cortical networks. Stability analysis of the linearized model and simulations of different degrees of complexity show that stability is only obtained for very fast and sufficiently strong inhibition; otherwise the network activity develops into synchronous oscillations with frequency and amplitude dynamics governed predominantly by the inhibition parameters, but largely independent of (1) the network architecture (uniform, random or structured), (2) the spiking or analog nature of the neural activity, and, albeit to a lesser extent, (3) the linear or nonlinear nature of the neural threshold function. Provided the network connectivity is sufficiently rich and structured, the spike activity exhibits features which resemble those observed in physiological recordings from various cortical areas: cell assembly behaviour with different, simultaneous correlation dynamics (event coherence and rate coherence)