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

## TL;DR

This paper investigates how weak noise influences neural oscillations in a bistable FitzHugh-Nagumo model, revealing noise-induced inhibition and modulation of spiking activity depending on initial conditions and system parameters.

## Contribution

It provides a detailed analysis of noise-induced transitions in neural dynamics, highlighting conditions for inhibition and modulation of oscillations in a bistable neuron model.

## Key findings

- Weak noise can inhibit neural spiking activity.
- Increasing noise strength can first inhibit then enhance spiking activity.
- The phenomenon depends on initial conditions and system parameters.

## Abstract

We analyze the effect of weak-noise-induced transitions on the dynamics of the FitzHugh-Nagumo neuron model in a bistable state consisting of a stable fixed point and a stable unforced limit cycle. Bifurcation and slow-fast analysis give conditions on the parameter space for the establishment of this bi-stability. In the parametric zone of bi-stability, weak-noise amplitudes may strongly inhibit the neuron's spiking activity. Surprisingly, increasing the noise strength leads to a minimum in the spiking activity, after which the activity starts to increase monotonically with increase in noise strength. We investigate this inhibition and modulation of neural oscillations by weak-noise amplitudes by looking at the variation of the mean number of spikes per unit time with the noise intensity. We show that this phenomenon always occurs when the initial conditions lie in the basin of attraction of the stable limit cycle. For initial conditions in the basin of attraction of the stable fixed point, the phenomenon however disappears, unless the time-scale separation parameter of the model is bounded within some interval. We provide a theoretical explanation of this phenomenon in terms of the stochastic sensitivity functions of the attractors and their minimum Mahalanobis distances from the separatrix isolating the basins of attraction.