NOISE-INDUCED BACKWARD BIFURCATIONS OF STOCHASTIC 3D-CYCLES / Bashkirtseva I.,Ryashko L.,Stikhin P. // FLUCTUATION AND NOISE LETTERS. - 2010. - V. 9, l. 1. - P. 89-106.

ISSN/EISSN:

0219-4775 / 1793-6780

Type:

Article

Abstract:

We study stochastically forced multiple limit cycles of nonlinear dynamical systems in a period-doubling bifurcation zone. Noise-induced transitions between separate parts of the cycle are considered. A phenomenon of a decreasing of the stochastic cycle multiplicity with a noise intensity growth is investigated. We call it by a backward stochastic bifurcation (BSB). In this paper, for the BSB analysis we suggest a stochastic sensitivity function technique. As a result, a method for the estimation of critical values of noise intensity corresponding to BSB is proposed. The constructive possibilities of this general method for the detailed BSB analysis of the multiple stochastic cycles of the forced Roessler system are demonstrated.

Author keywords:

Stochastic systems; limit cycles; bifurcations; Roessler system HOPF-BIFURCATION; SENSITIVITY-ANALYSIS; EXCITABLE SYSTEMS; DUFFING-VAN; CHAOS; MODEL; OSCILLATIONS; CYCLES; ORDER

DOI:

10.1142/S0219477510000095

Web of Science ID:

ISI:000275470000008

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
EISSN	1793-6780
Keywords-Plus	HOPF-BIFURCATION; SENSITIVITY-ANALYSIS; EXCITABLE SYSTEMS; DUFFING-VAN; CHAOS; MODEL; OSCILLATIONS; CYCLES; ORDER
Research-Areas	Mathematics; Physics
Web-of-Science-Categories	Mathematics, Interdisciplinary Applications; Physics, Applied
Author-Email	lev.ryashko@usu.ru
Funding-Acknowledgement	RFBR {[}09-01-00026, 09-08-00048]; Federal Education Agency {[}2.1.1/2571]; Federal Target Program {[}N 02.740.11.0202]
Funding-Text	This work was partially supported by grants RFBR09-01-00026, 09-08-00048, Federal Education Agency 2.1.1/2571, Federal Target Program N 02.740.11.0202.
Number-of-Cited-References	46
Usage-Count-Since-2013	5
Journal-ISO	Fluct. Noise Lett.
Doc-Delivery-Number	567TR