R. I. Kadiev, A. V. Ponosov, “Global stability of systems of nonlinear Itô differential equations with aftereffect and N.V. Azbelev's <nobr>$W$</nobr>-method”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, Number 1,Pages <nobr>38

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Global stability of systems of nonlinear Itô differential equations with aftereffect and N.V. Azbelev's $W$-method

R. I. Kadiev^ab, A. V. Ponosov^c

^a Daghestan Scientific Centre of Russian Academy of Sciences, M. Gadjieva str., 45, Makhachkala, 367032 Russia
^b Dagestan State University, 43 a Hajiyev str., Makhachkala, 367000, Russia
^c Norwegian University of Life Sciences, P.O. Box 5003 N-1432, As, Norway

Abstract: The work studies the global moment stability of solutions of systems of nonlinear differential Ito equations with delays. A modified regularization method ($W$ -method) for the analysis of various types of stability of such systems, based on the choice of the auxiliary equations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given.

Keywords: nonlinear Itô equations, stability of solutions, method of auxiliary equations, positive invertibility of matrices, bounded delays.

UDC: 517.929:519.21

Received: 30.03.2021
Revised: 19.04.2021
Accepted: 29.06.2021

DOI: 10.26907/0021-3446-2022-1-38-56