Numerical versus analytic synchronization in small-world networks of Hindmarsh-Rose neurons

Abstract

Neuronal temporal synchronization is one of the key issues in studying binding phenomenon in neural systems. In this paper we consider identical Hindmarsh-Rose neurons coupled over Newman-Watts small-world networks and investigate to what extent the numerical and analytic synchronizing coupling strengths are different. We use the master-stability-function approach to determine the unified coupling strength necessary for analytic synchronization. We also solve the network's differential equations numerically and track the synchronization error and consequently determine the numerical synchronizing coupling parameters. Then, we compare these two values and investigate the influence of various network parameters on the gap between them. We find that this gap is almost not influenced by network size. The only parameter that affects the gap between the analytic and numerical synchronizing parameters is the average degree, i.e. average connection per node in the connection graph. In networks with higher average degree this gap is larger than those with lower average degree. © Springer-Verlag Berlin Heidelberg 2009.