  A minimalistic model of the half-center oscillator is proposed. Within it, we
consider dynamics of two excitable neurons interacting by means of the
excitatory coupling. In the parameter space of the model, we identify the
regions of dynamics, characteristic for central pattern generators:
respectively, in-phase, anti-phase synchronous oscillations and quiescence, and
study various bifurcation transitions between all these states. Suggested model
can serve as a building block of specific complex central pattern generators
for studies of rhythmic activity and information processing in animals and
humans.
