Unpredictable solutions of Duffing type equations with Markov coefficients

Akhme M. Tleubergenova M. Zhamanshin A.
2023 SINUS Association

Carpathian Journal of Mathematics
2023 #39 Issue 3 569 - 582 pp.

The paper considers a stochastic differential equation of Duffing type with Markov coefficients. The existence of unpredictable solutions is considered. The unpredictability is a property of bounded functions characterized by unbounded sequences of moments of divergence and convergence in Bebutov dynamics. Markov components of the equation coefficients admit the unpredictability property. The components of the equation coefficients are derived from a Markov chain. The existence, uniqueness and exponential stability of an unpredictable solution are proved. The sequences of divergence and convergence of the coefficients and the solution are synchronized. Numerical examples that support the theoretical results are provided.

Duffing type , Markovian coefficients , stochastic differential equation , unpredictable solution

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Middle East Technical University, Department of Mathematics, Ankara, 06800, Turkey
Aktobe Regional State University, Department of Mathematics, Aktobe, 030000, Kazakhstan

Middle East Technical University
Aktobe Regional State University

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