Synchronization in a neuronal feedback loop through asymmetric temporal delays

¹  Department of Physics, Washington University in St. Louis - MO 63130-4899, USA
²  Fachbereich Physik, Universität Duisburg-Essen - Lotharstraße 1, 47048 Duisburg, Germany

Received: 7 March 2007
Accepted: 11 June 2007

Abstract

We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical value. We show that the angular frequency of the limit cycle is independent of an asymmetry in the delays. However, the delay asymmetry determines the phase difference between the periodic activities of the two components. Specifically, when the connection with negative coupling has a delay much larger than the delay for the positive coupling, the system approaches in-phase synchrony between the two components. Employing variational perturbation theory (VPT), we achieve an approximate analytical evaluation of the phase shift, in good agreement with numerical results.