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Updated: Feb 15, 2026

Stochastic Noise Application for the Assessment of Medial Vestibular Nucleus Neuron Sensitivity In Vitro
Published on: August 28, 2019
Noise-induced torus bursting in the stochastic Hindmarsh-Rose neuron model
Lev Ryashko1, Evdokia Slepukhina1
1Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, Ekaterinburg, Russia.
Abstract:
We study the phenomenon of noise-induced torus bursting on the base of the three-dimensional Hindmarsh-Rose neuron model forced by additive noise. We show that in the parametric zone close to the Neimark-Sacker bifurcation, where the deterministic system exhibits rapid tonic spiking oscillations, random disturbances can turn tonic spiking into bursting, which is characterized by the formation of a peculiar dynamical structure resembling that of a torus. This phenomenon is confirmed by the changes in dispersion of random trajectories as well as the power spectral density and interspike intervals statistics. In particular, we show that as noise increases, the system undergoes P and D bifurcations, transitioning from order to chaos. We ultimately characterize the transition from stochastic (tonic) spiking to bursting by stochastic sensitivity functions.
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