Stochastic Bifurcations and Noise-Induced Chaos in 3D Neuron Model / Bashkirtseva Irina,Fedotov Sergei,Ryashko Lev,Slepukhina Evdokia // INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. - 2016. - V. 26, l. 12.

ISSN/EISSN:
0218-1274 / 1793-6551
Type:
Article
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.
Author keywords:
Hindmarsh-Rose model; excitability; stochastic sensitivity; noise-induced transitions; stochastic generation of bursting oscillations; stochastic bifurcations; noise-induced chaotization HINDMARSH-ROSE MODEL; COHERENCE RESONANCE; PERTURBATIONS; SENSITIVITY; SYSTEMS; ORDER
DOI:
10.1142/S0218127416300329
Web of Science ID:
ISI:000389653800001
Соавторы в МНС:
Другие поля
Поле Значение
Month NOV
Publisher WORLD SCIENTIFIC PUBL CO PTE LTD
Address 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
Language English
Article-Number 1630032
EISSN 1793-6551
Keywords-Plus HINDMARSH-ROSE MODEL; COHERENCE RESONANCE; PERTURBATIONS; SENSITIVITY; SYSTEMS; ORDER
Research-Areas Mathematics; Science \& Technology - Other Topics
Web-of-Science-Categories Mathematics, Interdisciplinary Applications; Multidisciplinary Sciences
Author-Email Irina.Bashkirtseva@urfu.ru Sergei.Fedotov@manchester.ac.uk Lev.Ryashko@urfu.ru Evdokia.Slepukhina@urfu.ru
ORCID-Numbers Slepukhina, Evdokia/0000-0003-3523-6147
Funding-Acknowledgement Russian Science Foundation {[}16-11-10098]
Funding-Text The analysis of the deterministic HR model was carried out by S. Fedotov. The work on the stochastic analysis was carried out by I. Bashkirtseva, L. Ryashko and E. Slepukhina and supported by Russian Science Foundation (N 16-11-10098).
Number-of-Cited-References 38
Usage-Count-Last-180-days 3
Usage-Count-Since-2013 13
Journal-ISO Int. J. Bifurcation Chaos
Doc-Delivery-Number EE5NB