Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances / Bashkirtseva Irina,Ryashko Lev,Schurz Henri // CHAOS SOLITONS \& FRACTALS. - 2009. - V. 39, l. 1. - P. 72-82.

ISSN/EISSN:

0960-0779 / нет данных

Type:

Article

Abstract:

An analysis of the classical Hopf differential system perturbed by multiplicative and additive noises is carried out. An explicit representation for the stationary probability density function is found as an analytical solution of related Fokker-Planck equation. The difference in the response of Hopf systems perturbed by additive and multiplicative random noises is investigated. That difference can be seen in the zone of the transition from the trivial equilibrium point to noisy limit cycle. A delaying shift of the Hopf bifurcation point induced by multiplicative noise is recognized. In fact, an explicit formula of the radius of the stochastic limit cycle as a function of the involved parameters is stated. The phenomenon of inverse stochastic bifurcation in which auto-oscillations are suppressed by multiplicative noise is clearly observed. Eventually, the analytical description of the probability density of the randomly forced Hopf system offers the excellent possibility to test and compare the accuracy of different numerical schemes with respect to the replication of stochastic limit cycles. The superiority of the linear-implicit trapezoidal-type method is demonstrated in this respect. (C) 2007 Elsevier Ltd. All rights reserved.

Author keywords:

LIMIT-CYCLE; SENSITIVITY; BIFURCATION; LAWS; VAN

DOI:

10.1016/j.chaos.2007.01.128

Web of Science ID:

ISI:000264703700008

Соавторы в МНС:

Другие поля

Поле	Значение
Month	JAN 15
Publisher	PERGAMON-ELSEVIER SCIENCE LTD
Address	THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Language	English
Keywords-Plus	LIMIT-CYCLE; SENSITIVITY; BIFURCATION; LAWS; VAN
Research-Areas	Mathematics; Physics
Web-of-Science-Categories	Mathematics, Interdisciplinary Applications; Physics, Multidisciplinary; Physics, Mathematical
Author-Email	lev.ryashko@usu.ru
Funding-Acknowledgement	RFBR {[}06-01-00625, 06-08-00396, 07-01-96079-ural]
Funding-Text	This work was partially supported by RFBR Grants (06-01-00625, 06-08-00396, 07-01-96079-ural).
Number-of-Cited-References	29
Usage-Count-Since-2013	9
Journal-ISO	Chaos Solitons Fractals
Doc-Delivery-Number	426JJ