Neural Network Model Carrying Phase Information with Application to Collective Dynamics

Abstract

A network of periodically bursting model neurons is proposed. Its unique feature is a complex representation of the cell variables and also of the synaptic matrix. In the strong-coupling limit, the model recovers the traditional neural network model of simple on-off units, while in the weak-coupling limit it reduces to the network of smooth phase oscillators. In the special case of all-to-all excitatory coupling, some numerical and analytical evidence is provided for the occurrence of global phase locking. More complicated collective behavior such as clustering is also discovered numerically. Stimulus-evoked collective oscillations as observed in the cat primary visual cortex are explained within the present framework.