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Global Stability of Systems of Nonlinear Itô Differential Equations with Aftereffect and N.V. Azbelev’s W-Method

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Abstract

This work studies the global moment stability of solutions of systems of nonlinear Itô delay differential equations. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of an auxiliary equation and applications of the theory of positively invertible matrices, is proposed and justified. This method for deterministic functional differential equations was developed by N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for general and specific classes of Itô equations are presented.

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Funding

This work was supported in part by the Norwegian Research Council, grant no. 239070.

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Authors and Affiliations

  1. Dagestan Scientific Center, Russian Academy of Sciences, 367032, Makhachkala, Russia

    R. I. Kadiev

  2. Dagestan State University, 367000, Makhachkala, Russia

    R. I. Kadiev

  3. Norwegian University of Life Sciences, P.O. Box 5003, N-1432, As, Norway

    A. V. Ponosov

Authors
  1. R. I. Kadiev
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  2. A. V. Ponosov
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Correspondence to R. I. Kadiev or A. V. Ponosov.

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The authors declare that they have no conflicts of interest.

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Translated by E. Chernokozhin

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Kadiev, R.I., Ponosov, A.V. Global Stability of Systems of Nonlinear Itô Differential Equations with Aftereffect and N.V. Azbelev’s W-Method. Russ Math. 66, 31–45 (2022). https://doi.org/10.3103/S1066369X22010030

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