Dresden 2006 – scientific programme
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DY: Dynamik und Statistische Physik
DY 34: Nonlinear Dynamics, Synchronization and Chaos I
DY 34.2: Talk
Wednesday, March 29, 2006, 14:45–15:00, H\"UL 186
Nonperturbative Calculation of a Limit Cycle in a Two-Neuron System with Delayed Feedback — •Axel Pelster1, Sebastian Brandt2, Michael Schanz3, and Ralf Wessel2 — 1Fachbereich Physik, Universität Duisburg-Essen, Universitätsstraße 5, 45117 Essen, Germany — 2Physics Department, CB 1105 Washington University, 1 Brookings Drive, St. Louis, USA — 3IPVS, Universität Stuttgart, Universitätsstraße 38, 70569 Stuttgart, Germany
Neural circuits composed of a small number of neurons form the basic feedback mechanisms involved in the regulation of neural activity. We use a bifurcation analysis and numerical simulations in order to investigate a model system which consists of two Hopfield-like neurons with a time delayed feedback. It is described by the system of delay differential equations d u1/2(t)/dt = −u1/2(t) + a1/2 tanh[u2/1(t − τ)], where u1/2(t) denote the voltages of the Hopfield neurons at time t. If the delay τ exceeds a certain critical value τc, the trivial fix point at the origin looses its stability and a stable limit cycle emerges. Using the Poincaré-Lindstedt method, we calculate both period and amplitude of the limit cycle perturbatively. Then we perform a resummation of the respective perturbation series by applying variational perturbation theory and compare our nonperturbative analytic results with numerical simulations.