title: Stochastic sensitivity analysis of noise-induced suppression of firing and giant variability of spiking in a Hodgkin-Huxley neuron model.
abstract: We study the stochastic dynamics of a Hodgkin-Huxley neuron model in a regime of coexistent stable equilibrium and a limit cycle. In this regime, noise may suppress periodic firing by switching the neuron randomly to a quiescent state. We show that at a critical value of the injected current, the mean firing rate depends weakly on noise intensity, while the neuron exhibits giant variability of the interspike intervals and spike count. To reveal the dynamical origin of this noise-induced effect, we develop the stochastic sensitivity analysis and use the Mahalanobis metric for this four-dimensional stochastic dynamical system. We show that the critical point of giant variability corresponds to the matching of the Mahalanobis distances from attractors (stable equilibrium and limit cycle) to a three-dimensional surface separating their basins of attraction.
authors.affiliation: Department of Mathematics, Ural Federal University, Pr. Lenina 51, Ekaterinburg, Russia.
authors.forename: Irina
authors.initials: I
authors.lastname: Bashkirtseva
authors.affiliation: Department of Physics and Astronomy, Ohio University, Athens, Ohio 45701, USA.
authors.forename: Alexander B
authors.initials: AB
authors.lastname: Neiman
authors.affiliation: Department of Mathematics, Ural Federal University, Pr. Lenina 51, Ekaterinburg, Russia.
authors.forename: Lev
authors.initials: L
authors.lastname: Ryashko
mesh_terms: D008959:Models, Neurological; D009474:Neurons / Q000166:cytology*; D013269:Stochastic Processes