J. L. van Hemmen, W. Gerstner, and R. Ritz.
A `microscopic' model of collective oscillations in the cortex.
In: J. G. Taylor, E. K. Caianiello, R. N. J. Cotterell, and J. W. Clark (eds.) Neural network dynamics, pages 250-257, Springer, Berlin Heidelberg New York, 1992.

Abstract

The discovery of coherent oscillations in the primary visual cortex of the cat has aroused considerable theoretical interest. Most model networks that try to simulate these collective oscillations use some kind of oscillatory element as the basic unit of the network. It is, however, not clear how these oscillations should be described on a more microscopic level. Here we present a network that is based on a couple of measurable neurobiological quantities: (i) A distribution of axonal delay times for the transmission of spikes. (ii) A postsynaptic response described by realistic excitatory or inhibitory postsynaptic potentials (EPSP or IPSP). (iii) A threshold dynamics for the model neurons that includes refractoriness and noise. For a realistic set of parameters, the network shows collective oscillations only while an external signal is applied. If the parameters are changed significantly, other scenarios will result in which the behaviour is qualitatively different showing prolonged oscillations or no oscillations at all.