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Title: | Methods of Stochastic Analysis of Complex Regimes in the 3D Hindmarsh-Rose Neuron Model |
Authors: | Bashkirtseva, I. Ryashko, L. Slepukhina, E. |
Issue Date: | 2018 |
Publisher: | World Scientific Publishing Co. Pte Ltd |
Citation: | Bashkirtseva I. Methods of Stochastic Analysis of Complex Regimes in the 3D Hindmarsh-Rose Neuron Model / I. Bashkirtseva, L. Ryashko, E. Slepukhina // Fluctuation and Noise Letters. — 2018. — Vol. 17. — Iss. 1. — 1850008. |
Abstract: | A problem of the stochastic nonlinear analysis of neuronal activity is studied by the example of the Hindmarsh-Rose (HR) model. For the parametric region of tonic spiking oscillations, it is shown that random noise transforms the spiking dynamic regime into the bursting one. This stochastic phenomenon is specified by qualitative changes in distributions of random trajectories and interspike intervals (ISIs). For a quantitative analysis of the noise-induced bursting, we suggest a constructive semi-analytical approach based on the stochastic sensitivity function (SSF) technique and the method of confidence domains that allows us to describe geometrically a distribution of random states around the deterministic attractors. Using this approach, we develop a new algorithm for estimation of critical values for the noise intensity corresponding to the qualitative changes in stochastic dynamics. We show that the obtained estimations are in good agreement with the numerical results. An interplay between noise-induced bursting and transitions from order to chaos is discussed. © 2018 World Scientific Publishing Company. |
Keywords: | EXCITABILITY HINDMARSH-ROSE MODEL NOISE-INDUCED CHAOTIZATION NOISE-INDUCED TRANSITIONS STOCHASTIC BIFURCATIONS STOCHASTIC GENERATION OF BURSTING OSCILLATIONS STOCHASTIC SENSITIVITY |
URI: | http://elar.urfu.ru/handle/10995/75255 |
Access: | info:eu-repo/semantics/openAccess |
RSCI ID: | 35543883 |
SCOPUS ID: | 85040993681 |
WOS ID: | 000423192100009 |
PURE ID: | 6432051 |
ISSN: | 0219-4775 |
DOI: | 10.1142/S0219477518500086 |
metadata.dc.description.sponsorship: | The work was supported by Russian Science Foundation (N 16-11-10098). |
RSCF project card: | 16-11-10098 |
Appears in Collections: | Научные публикации ученых УрФУ, проиндексированные в SCOPUS и WoS CC |
Files in This Item:
File | Description | Size | Format | |
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10.1142-s0219477518500086.pdf | 6,32 MB | Adobe PDF | View/Open |
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