Spectral Statistics of Instantaneous Normal Modes in Liquids and Random Matrices

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 exitatory coupling. We show that the delay is dependent on the level of noise and suggest that a curious stochastic "anti-resonance" is present. <p> PACS numbers: 87.10.+e,87.18.Bb,87.18.Sn,87.19.La