  The influence of time delay in systems of two coupled excitable neurons is
studied in the framework of the FitzHugh-Nagumo model. Time-delay can occur in
the coupling between neurons or in a self-feedback loop. The stochastic
synchronization of instantaneously coupled neurons under the influence of white
noise can be deliberately controlled by local time-delayed feedback. By
appropriate choice of the delay time synchronization can be either enhanced or
suppressed. In delay-coupled neurons, antiphase oscillations can be induced for
sufficiently large delay and coupling strength. The additional application of
time-delayed self-feedback leads to complex scenarios of synchronized in-phase
or antiphase oscillations, bursting patterns, or amplitude death.
