A model for neuronal oscillations in the visual cortex. 1. Mean-field theory and derivation of the phase equations

We study a neural network consisting of model neurons whose efferent synapses are either excitatory or inhibitory. They are densely interconnected on a local scale, but only sparsely on a larger scale. The local clusters are described by the mean activities of excitatory and inhibitory neurons. The equations for these activities define a neuronal oscillator, which can be switched between an active and a passive state by an external input. Investigating the coupling of two of these oscillators we found their coupling behaviour to be activity-dependent. They are tightly coupled and almost synchronized if both oscillators are active, but weakly coupled if one or both oscillators are passive. This activity-dependent coupling is independent of the underlying connectivities, which are fixed. Finally, for coupled active oscillators we derive a simplified description by disregarding the amplitudes of the oscillators and working with their phases. We use this simplified description in a compagnion article to model the oscillations in the visual cortex.