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Analysis and Simulation of Nonlinear Stochastic Systems

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Nonlinear Dynamics in Engineering Systems

Abstract

The paper discusses the transition from deterministic to stochastic dynamic systems under external or internal excitations. For this purpose, we apply harmonic excitation models with frequency fluctuations by white noise and derive invariant measures as stationary solutions of associated Fokker-Planck equations. In case of periodic system solutions, the measures degenerate to singular distributions. They become regular for increasing frequency fluctuations. In particular, they determine Lyapunov exponents of systems with generalized parameter fluctuations.

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References

  1. Wedig, W: Vom Chaos zur Ordnung. GAMM-Mitteilungen, Heft 2 (1989) 3–31

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Author information

Authors and Affiliations

  1. Institute for Technical Mechanics, University of Karlsruhe, Deutschland

    Walter V. Wedig

Authors
  1. Walter V. Wedig
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Editor information

Editors and Affiliations

  1. Institute B of Mechanics, University of Stuttgart, Pfaffenwaldring 9, D-7000, Stuttgart 80, Germany

    W. Schiehlen

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© 1990 Springer-Verlag Berlin Heidelberg

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Wedig, W.V. (1990). Analysis and Simulation of Nonlinear Stochastic Systems. In: Schiehlen, W. (eds) Nonlinear Dynamics in Engineering Systems. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83578-0_42

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  • DOI: https://doi.org/10.1007/978-3-642-83578-0_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83580-3

  • Online ISBN: 978-3-642-83578-0

  • eBook Packages: Springer Book Archive

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