NOISE-INDUCED OSCILLATING BISTABILITY AND TRANSITION TO CHAOS IN FITZHUGH-NAGUMO MODEL / Bashkirtseva Irina,Ryashko Lev,Slepukhina Eudokia // FLUCTUATION AND NOISE LETTERS. - 2014. - V. 13, l. 1.

ISSN/EISSN:

0219-4775 / 1793-6780

Type:

Article

Abstract:

Stochastic dynamics of the FitzHugh-Nagumo (FHN) neuron model in the limit cycles zone is studied. For weak noise, random trajectories are concentrated in the small neighborhood of the unforced deterministic cycle. As the noise intensity increases, in the Canard-like cycles zone of the FHN model, a bundle of the stochastic trajectories begins to split into two parts. This phenomenon is investigated using probability density functions for the distribution of random trajectories. It is shown that the intensity of noise generating this splitting bifurcation significantly depends on the stochastic sensitivity of cycles. Using the stochastic sensitivity function (SSF) technique, we find a critical value of the parameter corresponding to the supersensitive cycle. For the neighborhood of this critical value, a comparative parametrical analysis of the phenomenon of the stochastic cycle splitting is performed. To predict the splitting bifurcation and estimate a threshold value of the noise intensity, we use a confidence domains method based on SSF. A phenomenon of the noise-induced chaotization is studied. We show that P-bifurcation of the splitting of stochastic cycles implies a D-bifurcation of a noise-induced chaotization.

Author keywords:

FitzHugh-Nagumo model; excitability; stochastic sensitivity; cycles; bifurcations; noise-induced chaotization STOCHASTIC RESONANCE; COHERENCE RESONANCE; EXCITABLE SYSTEMS; PERTURBATIONS; SENSITIVITY; STABILITY; 3D-CYCLES; IMPULSES; ORDER

DOI:

10.1142/S0219477514500047

Web of Science ID:

ISI:000333112600004

Соавторы в МНС:

Другие поля

Поле	Значение
Month	MAR
Publisher	WORLD SCIENTIFIC PUBL CO PTE LTD
Address	5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
Language	English
Article-Number	1450004
EISSN	1793-6780
Keywords-Plus	STOCHASTIC RESONANCE; COHERENCE RESONANCE; EXCITABLE SYSTEMS; PERTURBATIONS; SENSITIVITY; STABILITY; 3D-CYCLES; IMPULSES; ORDER
Research-Areas	Mathematics; Physics
Web-of-Science-Categories	Mathematics, Interdisciplinary Applications; Physics, Applied
Author-Email	lev.ryashko@usu.ru
ResearcherID-Numbers	Slepukhina, Evdokia/C-9624-2015
ORCID-Numbers	Slepukhina, Evdokia/0000-0003-3523-6147
Funding-Acknowledgement	Government of the Russian Federation {[}02.A03.21.0006]; RFBR {[}13-08-00069, 14-01-00181]
Funding-Text	This work was partially supported by the Government of the Russian Federation No: 02.A03.21.0006 (27.08.2013) and RFBR (13-08-00069, 14-01-00181).
Number-of-Cited-References	42
Usage-Count-Last-180-days	2
Usage-Count-Since-2013	24
Journal-ISO	Fluct. Noise Lett.
Doc-Delivery-Number	AD3BR