Stochastic generation of bursting oscillations in the spiking region of a 3D neuron model with the Lukyanov-Shilnikov bifurcation

Abstract

A stochastic three-dimensional neuron model with the Lukyanov-Shilnikov bifurcation is studied. We show that in the parameter region where the deterministic system exhibits tonic spiking regime with a single stable limit cycle, noise can induce bursting activity. This stochastic phenomenon is confirmed by changes in spacial and temporal characteristics of oscillations. The probabilistic mechanism of the stochastic generation of bursting is studied by means of the stochastic sensitivity functions and Mahalanobis metrics. © 2022 Author(s).