Stability of Synchronous Solutions in Weakly Coupled Neuron Networks

Abstract

The stability of synchronous solutions for weakly coupled two-neuron networks is examined. It is well known that for a pair of identical neurons with a weak, reciprocal connection, there always exists a synchronous solution, the stability of which depends on both intrinsic cell properties and the connection type. By considering several neuronal models, all of which possess a Type-I phase-response function, the manners in which the form of the phase-response function and the neuronal coupling affect the stability of the synchronous solution are investigated, and the properties necessary for stable synchrony in these models are described in detail.