Highly Influenced

# Variational calculation of the limit cycle and its frequency in a two-neuron model with delay.

@article{Brandt2006VariationalCO, title={Variational calculation of the limit cycle and its frequency in a two-neuron model with delay.}, author={Sebastian F. Brandt and Axel Pelster and Ralf Wessel}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2006}, volume={74 3 Pt 2}, pages={036201} }

- Published 2006 in Physical review. E, Statistical, nonlinear, and…

We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle emerges via a supercritical Hopf bifurcation. First, we calculate its frequency and trajectory perturbatively by applying the Poincaré-Lindstedt method. Then, the perturbation series are resummed by means of the Shohat expansion in good agreement with numerical… CONTINUE READING