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We analyze the effect of weak-noise-induced transitions on the dynamics ofthe FitzHugh-Nagumo neuron model in a bistable state consisting of a stablefixed point and a stable unforced limit cycle. Bifurcation and slow-fastanalysis give conditions on the parameter space for the establishment of thisbi-stability. In the parametric zone of bi-stability, weak-noise amplitudes maystrongly inhibit the neuron's spiking activity. Surprisingly, increasing thenoise strength leads to a minimum in the spiking activity, after which theactivity starts to increase monotonically with increase in noise strength. Weinvestigate this inhibition and modulation of neural oscillations by weak-noiseamplitudes by looking at the variation of the mean number of spikes per unittime with the noise intensity. We show that this phenomenon always occurs whenthe initial conditions lie in the basin of attraction of the stable limitcycle. For initial conditions in the basin of attraction of the stable fixedpoint, the phenomenon however disappears, unless the time-scale separationparameter of the model is bounded within some interval. We provide atheoretical explanation of this phenomenon in terms of the stochasticsensitivity functions of the attractors and their minimum Mahalanobis distancesfrom the separatrix isolating the basins of attraction.

Weak-noise-induced transitions with inhibition and modulation of neural oscillations