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The random attractor of the stochastic Lorenz system

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Abstract.

We study the existence of attractors for dynamical systems under the influence of random parameters. Such a random attractor is a measurable multi-function with compact images fulfilling particular invariance and attracting properties. In particular, this uniquely determined attractor attracts measurable multi-functions. Under certain conditions we estimate the Hausdorff dimension of the attractor. These results will be applied to the Lorenz system under the influence of a random external parameter perturbation.

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Authors and Affiliations

  1. FB Angewandte Naturwissenschaften, FH Merseburg, Geusaer Straße, 06217 Merseburg, Germany, e-mail: schmalfuss@in.fh-merseburg.de, , , , , , DE

    B. Schmallfuß

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  1. B. Schmallfuß
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Received: March 27, 1996; revised: December and March 1997

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Schmallfuß, B. The random attractor of the stochastic Lorenz system. Z. angew. Math. Phys. 48, 951–975 (1997). https://doi.org/10.1007/s000330050074

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  • DOI: https://doi.org/10.1007/s000330050074

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