Confidence tori in the analysis of stochastic 3D-cycles / Ryashko L.,Bashkirtseva I.,Gubkin A.,Stikhin P. // MATHEMATICS AND COMPUTERS IN SIMULATION. - 2009. - V. 80, l. 2. - P. 256-269.

ISSN/EISSN:

0378-4754 / 1872-7166

Type:

Article

Abstract:

We present a new computer approach to the spatial analysis of stochastically forced 3D-cycles in nonlinear dynamic systems. This approach is based on a stochastic sensitivity analysis and uses the construction of confidence tori. A confidence torus as a simple 3D-model of the stochastic cycle adequately describes its main probabilistic features. We suggest an effective algorithm for construction of the confidence tori using a discrete set of confidence ellipses. The ability of these tori to visualize thin effects observed for the period-doubling bifurcations zone in the stochastic Roessler model are shown. For this zone, the geometrical growth of stochastic sensitivity of the forced cycles under transition to chaos is presented. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.

Author keywords:

Stochastic systems; Cycles; Stochastic sensitivity; Roessler model SENSITIVITY-ANALYSIS; HOPF-BIFURCATION; EXTERNAL NOISE; LORENZ MODEL; LIMIT-CYCLE; CHAOS; FLUCTUATIONS; SYSTEMS; AMPLIFICATION; ATTRACTORS

DOI:

10.1016/j.matcom.2009.06.026

Web of Science ID:

ISI:000271252500002

Соавторы в МНС:

Другие поля

Поле	Значение
Month	OCT
Publisher	ELSEVIER SCIENCE BV
Address	PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Language	English
EISSN	1872-7166
Keywords-Plus	SENSITIVITY-ANALYSIS; HOPF-BIFURCATION; EXTERNAL NOISE; LORENZ MODEL; LIMIT-CYCLE; CHAOS; FLUCTUATIONS; SYSTEMS; AMPLIFICATION; ATTRACTORS
Research-Areas	Computer Science; Mathematics
Web-of-Science-Categories	Computer Science, Interdisciplinary Applications; Computer Science, Software Engineering; Mathematics, Applied
Author-Email	lev.ryashko@usu.ru
Funding-Acknowledgement	RFBR {[}09-01-00026, 09-08-00048]; Federal Education Agency {[}2.1.1/2571]
Funding-Text	This paper is partially supported by grants RFBR 09-01-00026, 09-08-00048 and Federal Education Agency 2.1.1/2571.
Number-of-Cited-References	45
Usage-Count-Since-2013	4
Journal-ISO	Math. Comput. Simul.
Doc-Delivery-Number	512MC