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Stability of solutions of a system of linear differential equations with periodic stochastic coefficients

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Abstract

Systems of equations for first and second moments are investigated and transformed. Stability of solutions of a first-order linear differential equations is analyzed. Stability of solutions of the stochastic Mathieu equation is investigated and the boundaries of the instability region are determined.

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Literature cited

  1. K. G. Valeev and O. A. Zhautykov, Infinite Systems of Differential Equations [in Russian], Nauka, Alma-Ata (1974).

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  3. S. M. Khrisanov, “Lyapunov exponents of linear systems with Markov coefficients,” Prikl. Mat. Mekh.,47, No. 1, 81–87 (1983).

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  4. S. M. Khrisanov, “The set of moment systems,” Ukr. Math. Zh.,33, No. 6, 787–792 (1981).

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Authors and Affiliations

  1. Kiev Institute of National Economy and Ukrainian Agricultural Academy, USSR

    K. G. Valeev & I. M. Sulima

Authors
  1. K. G. Valeev
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  2. I. M. Sulima
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 119–126, 1986.

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Valeev, K.G., Sulima, I.M. Stability of solutions of a system of linear differential equations with periodic stochastic coefficients. J Math Sci 58, 486–491 (1992). https://doi.org/10.1007/BF01100080

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  • DOI: https://doi.org/10.1007/BF01100080

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