  We report a noise induced delay of bifurcation in a simple pulse-coupled
neural circuit. We study the behavior of two neural oscillators, each
individually governed by saddle-node dynamics, with reciprocal excitatory
synaptic connections. In the deterministic circuit, the synaptic current
amplitude acts as a control parameter to move the circuit from a mono-stable
regime through a bifurcation into a bistable regime. In this regime stable
sustained anti-phase oscillations in both neurons coexist with a stable rest
state. We introduce a small amount of random current into both neurons to model
possible randomly arriving synaptic inputs. We find that such random noise
delays the onset of bistability, even though in decoupled neurons noise tends
to advance bifurcations and the circuit has only excitatory coupling. We show
that the delay is dependent on the level of noise and suggest that a curious
stochastic ``anti-resonance'' is present.
