Physica D: Nonlinear Phenomena, Vol. 114 (1-2) (1998) pp. 147-171

Synchronization in two neurons

Results for a two-component dynamical model with time-delayed inhibition

Gilles Renverseza

a Centre de Physique Théorique, UPR 7061 du Centre National de la Recherche Scientifique, Campus de Luminy, Case 907, 13288 Marseille Cedex 9, France


We study synchronization in two neurons using two-dimensional neuronal models coupled through threshold delayed inhibition, acting for a fixed duration T. We explain the mechanism of synchronization between the two coupled units by means of phase-plane analysis. Using a piecewise linear approximation, we compute the firing times of two mutually coupled neurons, which allows a quantitative study of synchronization. The results are in good agreement, both quantitatively and qualitatively, with the numerical simulations of the full nonlinear coupled system describing the two neurons. We first show that, with simple inhibition, only phase-lagged synchronization can be achieved except for a particular set of T-values. We then show that coincidence synchronization can rapidly be achieved with an improved coupling model which takes into account the increase of membrane conductance during inhibition.

PACS Classification: 02.30.Ks; 05.45.+b; 87.10.+e

Keyword(s): Neuronal modelling; Synchronization; Inhibition; Time-delayed coupling; Phase-plane analysis