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Stability and Invariant Measures of Perturbed Dynamical Systems

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IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics

Part of the book series: Solid Mechanics and its Applications ((SMIA,volume 47))

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Abstract

For stability investigations of perturbed dynamical systems it is suitable to utilize the associated invariant measures in order to determine Lyapunov exponents of higher numerical accuracy. The densities of the invariant measures can be calculated by the stationary solutions of Fokker-Planck equations. The paper presents iterative schemes to solve these parabolic equations numerically and check the obtained results by means of Monte-Carlo simulations. Both methods are applied to oscillators perturbed by non-normal processes with bounded realizations.

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References

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Author information

Authors and Affiliations

  1. University of Karlsruhe, D-76128, Karlsruhe, Germany

    Walter V. Wedig

Authors
  1. Walter V. Wedig
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Editor information

Editors and Affiliations

  1. Department of Structural Engineering, Norwegian University of Science and Technology, Trondheim, Norway

    A. Naess

  2. Division of Mechanics, Lund Institute of Technology, Lund University, Sweden

    S. Krenk

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© 1996 Kluwer Academic Publishers

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Wedig, W.V. (1996). Stability and Invariant Measures of Perturbed Dynamical Systems. In: Naess, A., Krenk, S. (eds) IUTAM Symposium on Advances in Nonlinear Stochastic Mechanics. Solid Mechanics and its Applications, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0321-0_42

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  • DOI: https://doi.org/10.1007/978-94-009-0321-0_42

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6630-3

  • Online ISBN: 978-94-009-0321-0

  • eBook Packages: Springer Book Archive

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