Abstract
We present a new proof for criteria for the asymptotic stability of systems of difference and differential equations based on the properties of monotone operators in a semiordered space. We also establish necessary and sufficient conditions for the asymptotic stability of stochastic systems of differential and difference equations in the mean square.
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REFERENCES
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D. G. Korenevskii, Stability of Solutions of Deterministic and Stochastic Differential-Difference Systems of Equations[in Russian], Naukova Dumka, Kiev (1992).
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Valeev, K.G., Dzhalladova, I.A. Criteria for the Asymptotic Stability of Solutions of Dynamical Systems. Ukrainian Mathematical Journal 52, 1942–1948 (2000). https://doi.org/10.1023/A:1010464128307
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DOI: https://doi.org/10.1023/A:1010464128307