Connectivity and phase coherence in neural network models of interconnected Z<sup>4</sup>-bi-stable units

Abstract

A phenomenological neural network model with bi-stable oscillatory units is used to model up- and down-states. These states have been observed in vivo in biological neuronal systems and feature oscillatory, limit cycle type of behavior in the up-states. A network is formed by a set of interconnected units. Two different types of network layouts are considered in this work: networks with hierarchical connections and hubs and networks with random connections. The phase coherence between the different units is analyzed and compared to the connectivity distance between nodes. In addition the connectivity degree of a node is associated to the average phase coherence with all other units. The results show that we may be able to identify the set of hubs in a network based on the phase coherence estimates between the different nodes. If the network is very dense or randomly connected, the underlying network structure, however, can not be derived uniquely from the phase coherence.