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Random attractors for ambiguously solvable systems dissipative with respect to probability

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Abstract

We prove a theorem on the existence of a random attractor for a multivalued random dynamical system dissipative with respect to probability. Abstract results are used for the analysis of the qualitative behavior of solutions of a system of ordinary differential equations with continuous right-hand side perturbed by a stationary random process. In terms of the Lyapunov function, for an unperturbed system, we give sufficient conditions for the existence of a random attractor.

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REFERENCES

  1. L. Arnold (1998) Random Dynamical Systems Springer Berlin

    Google Scholar 

  2. H. Crauel F. Flandoli (1994) ArticleTitleAttractors for random dynamical systems Probab. Theory Related Fields 100 365–393

    Google Scholar 

  3. H. Crauel (1999) ArticleTitleGlobal random attractors are uniquely determined by attracting deterministic compact sets Ann. Mat. Pura Appl. 126 IssueID4 57–72

    Google Scholar 

  4. K. R. Schenk-Hoppe (1998) ArticleTitleRandom attractors — general properties, existence and applications to stochastic bifurcation theory Discr. Cont. Dynam. Syst. 4 IssueID1 99–130

    Google Scholar 

  5. A. V. Kapustyan V. S. Mel’nik (1998) ArticleTitleAttractors of multivalued semidynamical systems and their approximations Dopov. Nats. Akad. Nauk Ukr. 10 21–25

    Google Scholar 

  6. T. Caraballo J. A. Langa J. Valero (2002) ArticleTitleGlobal attractors for multivalued random dynamical systems Nonlin. Analysis 48 805–829

    Google Scholar 

  7. R. Z. Khas’minskii (1969) Stability of Systems of Differential Equations under Random Perturbations of Their Parameters Nauka Moscow

    Google Scholar 

  8. J.-P. Aubin H. Frankowska (1990) Set-Valued Analysis Birkhäuser Boston

    Google Scholar 

  9. A. F. Fillipov (1985) Differential Equations with Discontinuous Right-Hand Side Nauka Moscow

    Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 892–900, July, 2004.

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Kapustyan, O.V. Random attractors for ambiguously solvable systems dissipative with respect to probability. Ukr Math J 56, 1063–1073 (2004). https://doi.org/10.1007/PL00022177

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