Abstract not found

. Coupled oscillator models use a single phase variable to approximate the voltage oscillation of each neuron during repetitive firing where the behavior of the model depends on the connectivity and the interaction function chosen to describe the coupling. We introduce a network model consisting of a continuum of these oscillators which includes the effects of spatially decaying coupling and axonal delay. We derive equations for determining the stability of solutions and analyze the network behavior for two different interaction functions. The first is a sine function and the second is derived from a compartmental model of a pyramidal cell. In both cases, the system of coupled neural oscillators can undergo a bifurcation from synchronous oscillations to waves. The change in qualitative behavior is due to the axonal delay which causes distant connections to encourage a phase shift between cells. We suggest that this mechanism could contribute to the behavior observed in several neurobi...

In this review, models of cortical associative memory with a background in Hebb's cell assembly hypothesis will be discussed. One mathematical realization of a Hebbian cell assembly is a recurrent artificial neural network. These recurrent attractor networks have several favorable features when used as models of cortical associative memory and they have been used to describe several cortical functions including models of olfactory and motor cortex, EEG and field potentials, psychology of memory retrieval and language deficits.