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Stability of Nonlinear Differential Systems with Right-Hand Side Depending on Markov’s Process

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Differential and Difference Equations with Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 47))

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Abstract

In this paper we investigated sufficient conditions for stability of solutions of systems of nonlinear differential equations with right-hand side depending on Markov’s process. The basic role in proof has Lyapunov functions. Nontrivial illustrative example is given.

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References

  1. Capiński, M., Zastawniak, T.: Probability Through Problems. Springer, New York (2003). ISBN 0-387-950063-X

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  2. Dzhalladova, I.A.: Stochastic Lyapunov’s functions functions for the non-linear differential equations. Ukr. Math. J. 54(1), 13 (2002)

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  3. Dzhalladova, I.A.: Optimization of Stochastic Systems, pp. 284. KNEU Press, Kiev (2005) (in Ukraine)

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  4. Gusak, D., Kukush, A., Kulik, A., Mishura, Y., Pilipenko, A.: Theory of Stochastic Processes. Springer, New York (2010). ISBN 978-0-387-87861-4

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  5. Tikhonov, V.I., Mironov, M.A.: Markov’s Processes, pp. 488. Sov. Radio, Moscow (1977) (in Russian)

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Correspondence to Irada Dzhalladova .

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Dzhalladova, I. (2013). Stability of Nonlinear Differential Systems with Right-Hand Side Depending on Markov’s Process. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_30

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