Analysis of stability in quadratic mean of the limit cycles of nonlinear stochastic systems / Gubkin A. A.,Ryashko L. B. // AUTOMATION AND REMOTE CONTROL. - 2007. - V. 68, l. 10. - P. 1801-1812.

ISSN/EISSN:

0005-1179 / нет данных

Type:

Article

Abstract:

Consideration was given to the exponential stability in quadratic mean of the stochastically perturbed limit cycles of the nonlinear systems. An approach was developed using the spectral theory of positive operators for the stability analysis. Within the framework of this approach, a positive operator of stochastic stability is assigned to the limit cycle. The spectral radius of this operator characterizes stability of the limit cycle. An iterative numerical method was proposed for calculation of the spectral radius of the stochastic stability operator, and a theorem about its convergence was proved. The constructive potentialities of the results obtained were demonstrated by the example of bifurcational analysis of the stochastic Ressler system at transition to chaos by multiple duplication of the limit cycle period.

Author keywords:

нет данных

DOI:

10.1134/S0005117907100086

Web of Science ID:

ISI:000250579400008

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	OCT
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
Research-Areas	Automation \& Control Systems; Instruments \& Instrumentation
Web-of-Science-Categories	Automation \& Control Systems; Instruments \& Instrumentation
Number-of-Cited-References	9
Usage-Count-Since-2013	2
Journal-ISO	Autom. Remote Control
Doc-Delivery-Number	226HG