  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
Poincar\'e-Lindstedt method. Then, the perturbation series are resummed by
means of the Shohat expansion in good agreement with numerical values. However,
with increasing delay, the accuracy of the results from the Shohat expansion
worsens. We thus apply variational perturbation theory (VPT) to the
perturbation expansions to obtain more accurate results, which moreover hold
even in the limit of large delays.
