Regensburg 2007 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 2: Time-delayed feedback and neural networks
DY 2.3: Vortrag
Montag, 26. März 2007, 11:00–11:15, H3
Controlling the Phase in a Neuronal Feedback Loop Through Asymmetric Temporal Delays — Sebasitan Brandt1, •Axel Pelster2, and Ralf Wessel1 — 1Department of Physics, Campus Box 1105, Washington University in St. Louis, MO 63130-4899, USA — 2Fachbereich Physik, Campus Duisburg, Universität Duisburg-Essen, 47048 Duisburg, Germany
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, we achieve an approximate analytical evaluation of the phase shift, in good agreement with numerical results.