Order and chaos in the stochastic Hindmarsh-Rose model of the neuron bursting / Bashkirtseva Irina,Ryashko Lev,Slepukhina Evdokia // NONLINEAR DYNAMICS. - 2015. - V. 82, l. 1-2. - P. 919-932.

ISSN/EISSN:

0924-090X / 1573-269X

Type:

Article

Abstract:

We study the stochastic dynamics of the two-dimensional Hindmarsh-Rose model. In the deterministic case, this system demonstrates mono- and bi-stable dynamic regimes. In the parametric zone of the coexisting stable equilibrium and limit cycle, the phenomenon of noise-induced transitions between the attractors is studied. In another parametric region, where the deterministic system has the only stable equilibrium, the stochastic generation of high-amplitude oscillations is also observed. We show that under the random disturbances, the system demonstrates noise-induced bursting: an alternation of small fluctuations near the equilibrium and high-amplitude oscillations. For the quantitative analysis of noise-induced bursting, an approach combining stochastic sensitivity function technique and confidence domains method is suggested. Constructive abilities of this method for the estimation of critical values for noise intensity corresponding to the qualitative changes in stochastic dynamics are demonstrated and confirmed by the good agreement with the direct numerical simulation. An interplay between noise-induced bursting and mutual transformations ``order-chaos{''} is discussed.

Author keywords:

Hindmarsh-Rose model; Excitability; Stochastic sensitivity; Noise-induced bursting; Chaos COHERENCE RESONANCE; NOISE; SYSTEMS; PERTURBATIONS; EXCITABILITY; OSCILLATIONS; SENSITIVITY

DOI:

10.1007/s11071-015-2206-y

Web of Science ID:

ISI:000362578100070

Соавторы в МНС:

Другие поля

Поле	Значение
Month	OCT
Publisher	SPRINGER
Address	VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS
Language	English
EISSN	1573-269X
Keywords-Plus	COHERENCE RESONANCE; NOISE; SYSTEMS; PERTURBATIONS; EXCITABILITY; OSCILLATIONS; SENSITIVITY
Research-Areas	Engineering; Mechanics
Web-of-Science-Categories	Engineering, Mechanical; Mechanics
Author-Email	Lev.Ryashko@urfu.ru
ORCID-Numbers	Slepukhina, Evdokia/0000-0003-3523-6147
Funding-Acknowledgement	Ministry of Education and Science of the Russian Federation {[}N 315]; RFBR {[}14-01-00181]
Funding-Text	This work was partially supported by the Ministry of Education and Science of the Russian Federation under the project N 315, and RFBR (14-01-00181).
Number-of-Cited-References	41
Usage-Count-Last-180-days	3
Usage-Count-Since-2013	16
Journal-ISO	Nonlinear Dyn.
Doc-Delivery-Number	CT1RK