Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect
https://doi.org/10.26907/0021-3446-2024-7-63-76
Abstract
The paper studies the global moment stability of systems of nonlinear Itô differential equations with delays. The analysis is done by a modified regularization method, known as the W-method, and based on the use of some auxiliary equation with subsequent application of the theory of positively invertible matrices. Sufficient conditions for the global asymptotic moment stability for both sufficiently general and specific systems of Ito equations formulated in terms of parameters of these systems are given. Connections between this stability and the properties of the delay functions are established.
About the Authors
R. I. Kadiev
Dagestan Federal Research Center of the Russian Academy of Sciences; Dagestan State University
Russian Federation
Russian Federation
Ramazan I. Kadiev.
45 M. Hajiyev str., Makhachkala, 367000; 43 a M. Hajiyev str., Makhachkala, 367000
A. V. Ponosov
Norwegian University of Life Sciences
Norway
Norway
Arcady V. Ponosov.
P.O. Box 5003 N-1432, As
References
1. Колмановский В.Б., Носов В.Р. Устойчивость и периодические режимы регулируемых систем с последействием (Наука, М., 1981).
2. Царьков Е.Ф. Случайные возмущения дифференционально-функциональных уравнений (Зинатне, Рига, 1989).
3. Мао X. Stochastic differential equations and applications (Horwood Publ. Ltd., Chichester, 1997).
4. Mohammed S.-E.F. Stochastic Functional Differential Equations With Memory. Theory, Examples and Applications, Proc. The Sixth Workshop on Stochastic Anal. (Geilo, Norway, 1996).
5. Azbelev N.V., Simonov P.M. Stability of differential equations with aftereffect (Taylor Erancis, London, 2003).
6. Azbelev N.V., Maksimov V.P., Rakhmatullina L.F. Introduction to the theory of functional differential equations: methods and applications (Hindawi, New York, 2007).
7. Кадиев Р.И., Поносов А.В. Глобальная устойчивость систем нелинейных дифференциалных уравнений Ито с последействием и W-метод Н.В. Азбелева, Изв. вузов. Матем. (1), 38-56 (2022).
8. Kadiev R., Ponosov A. Lyapunov stability of the generalized stochastic pantograph equation, J. Math., Article ID 7490936, 1-10 (2018).
9. Кадиев Р.И. Существование и единственность решения задачи Коши для функциональнодифференциальных уравнений по семимартингалу, Изв. вузов. Матем. (10), 35-39 (1995).
10. Веллман Р. Введение в теорию матриц (Наука, М., 1969).
11. Кадиев Р.И. Устойчивость решений стохастических функционально-дифференциальных уравнений, Дисс. . . . д-ра физ.-матем. наук (Махачкала, 2000).
Review
For citations:
Kadiev R.I., Ponosov A.V. Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(7):63-76. (In Russ.) https://doi.org/10.26907/0021-3446-2024-7-63-76
Views:
103
Email this article 