Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102182
Title: Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model
Authors: Bashkirtseva, I.
Fedotov, S.
Ryashko, L.
Slepukhina, E.
Issue Date: 2016
Publisher: World Scientific Publishing Co. Pte Ltd
Citation: Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model / I. Bashkirtseva, S. Fedotov, L. Ryashko, et al. — DOI 10.1142/S0218127416300329 // International Journal of Bifurcation and Chaos. — 2016. — Vol. 26. — Iss. 12. — 1630032.
Abstract: The stochastically forced three-dimensional Hindmarsh-Rose model of neural activity is considered. We study the effect of random disturbances in parametric zones where the deterministic model exhibits mono- and bistable dynamic regimes with period-adding bifurcations of oscillatory modes. It is shown that in both cases the phenomenon of noise-induced bursting is observed. In the monostable zone, where the only attractor of the system is a stable equilibrium, this effect is connected with a stochastic generation of large-amplitude oscillations due to the high excitability of the model. In a parametric zone of coexisting stable equilibria and limit cycles, bursts appear due to noise-induced transitions between the attractors. For a quantitative analysis of the noise-induced bursting and corresponding stochastic bifurcations, an approach based on the stochastic sensitivity function (SSF) technique is applied. Our estimations of the strength of noise that generates such qualitative changes in stochastic dynamics are in a good agreement with the direct numerical simulation. A relationship of the noise-induced generation of bursts with transitions from order to chaos is discussed. © 2016 World Scientific Publishing Company.
Keywords: EXCITABILITY
HINDMARSH-ROSE MODEL
NOISE-INDUCED CHAOTIZATION
NOISE-INDUCED TRANSITIONS
STOCHASTIC BIFURCATIONS
STOCHASTIC GENERATION OF BURSTING OSCILLATIONS
STOCHASTIC SENSITIVITY
BIFURCATION (MATHEMATICS)
GAUSSIAN NOISE (ELECTRONIC)
NEURONS
STOCHASTIC MODELS
BURSTING OSCILLATIONS
CHAOTIZATION
EXCITABILITY
HINDMARSH-ROSE MODEL
NOISE-INDUCED TRANSITION
STOCHASTIC BIFURCATION
STOCHASTIC SENSITIVITY
STOCHASTIC SYSTEMS
URI: http://hdl.handle.net/10995/102182
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 84996551429
PURE ID: 1306729
df3645fb-2ac4-4007-9db3-f53b8ab6da08
ISSN: 2181274
DOI: 10.1142/S0218127416300329
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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