Unpredictable solutions of Duffing type equations with Markov coefficients

Akhme M., Tleubergenova M., Zhamanshin A.

Carpathian Journal of Mathematics, vol.39, no.3, pp.569-582, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.37193/cjm.2023.03.01
  • Journal Name: Carpathian Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.569-582
  • Keywords: Duffing type, Markovian coefficients, stochastic differential equation, unpredictable solution
  • Middle East Technical University Affiliated: Yes

Abstract

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.