Pattern recognition and synchronization in pulse-coupled neural networks

This paper establishes and studies equations of a network that is composed of neurons with their dendrites and axons. The pulse generation in the axon is described by means of phase oscillators, whereas the dendritic currents are described by linear damping equations with source terms as which the incoming pulses act. The equations take into account delays and noise. In the case of phase-locking the equations have been solved previously by the author. The main objective of the present paper is to study in how far these equations may serve for pattern recognition. It is shown that either a random phase approximation for the stored patterns or a triple interaction term suffice to treat pattern recognition. It is pointed out how then recognized patterns can be either encoded as completed prototype patterns or as phase-locked states. It is suggested that to understand pattern recognition it is not only necessary to consider the whole network instead of "grandmother" cells but equally well the whole intermediate steps.