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Russia Izhevsk
Section Mathematics
Title About asymptotical properties of solutions of difference equations with random parameters
Author(-s) Rodina L.I.a, Tyuteev I.I.a
Affiliations Udmurt State Universitya
Abstract We investigate the asymptotic behavior of solutions of difference equations. Their right-hand sides at given time depend not only on the value of state at the previous moment, but also on a random value from a given set $\Omega$. We obtain conditions of Lyapunov stability and asymptotic stability of the equilibrium for all values of random parameters and with probability one. We show that the problem of coexistence of stochastic cycles of different periods has a solution, which strongly differs from a known Sharkovsky result for a determined difference equation. Under some conditions, the existence of a stochastic cycle of length $k$ implies the existence of a cycle of any length $\ell>k$.
Keywords difference equations with random parameters, Lyapunov stability, asymptotical stability, cyclic solution
UDC 517.935, 517.938
MSC 34A60, 37N35, 49J15, 93B03
DOI 10.20537/vm160107
Received 20 January 2016
Language Russian
Citation Rodina L.I., Tyuteev I.I. About asymptotical properties of solutions of difference equations with random parameters, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 1, pp. 79-86.
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