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

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 an 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 timescale 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.

journal_name

Biol Cybern

journal_title

Biological cybernetics

authors

Yamakou ME,Jost J

doi

10.1007/s00422-018-0770-1

subject

Has Abstract

pub_date

2018-10-01 00:00:00

pages

445-463

issue

5

eissn

0340-1200

issn

1432-0770

pii

10.1007/s00422-018-0770-1

journal_volume

112

pub_type

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