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Chaos in Nonlinear Systems Subjected to Small Random Perturbations

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Nonlinear Stochastic Dynamic Engineering Systems

Part of the book series: IUTAM Symposium ((IUTAM))

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Summary

Properties of dynamical behavior of nonlinear systems exhibiting chaos are investigated, under small random perturbations. Chaotic properties of deterministic systems modeled by a one-dimensional mapping are analyzed when the system is perturbed by a multiplicative and an additive noise. Stochastic versions of invariant measure and Lyapunov exponent are calculated and are comparatively discussed with deterministic ones, from the viewpoint of conservation of chaotic properties under small random perturbations. Finally, a different type of stochastic systems is shown to be equivalent to a deterministic system with chaotic behavior in some stochastic sense.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Production Engineering, Kyoto Institute of Technology, Japan

    Y. Sunahara & Y. Morita

  2. Department of Mechanical Engineering, Shiga Prefectural Junior College, Japan

    T. Yasuda

Authors
  1. Y. Sunahara
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  2. Y. Morita
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  3. T. Yasuda
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Editor information

Editors and Affiliations

  1. Österreichisches Nationalkomitee für Theoretische und Angewandte Mechanik, Technische Universität Wien, Institut für Allgemeine Mechanik, Karlsplatz 13/201, A-1040, Wien, Österreich

    F. Ziegler

  2. Institut für Mechanik, Universität Innsbruck, Technikerstraße 13, A-6020, Innsbruck, Österreich

    G. I. Schuëller Ph. D.

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© 1988 Springer-Verlag Berlin Heidelberg

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Sunahara, Y., Morita, Y., Yasuda, T. (1988). Chaos in Nonlinear Systems Subjected to Small Random Perturbations. In: Ziegler, F., Schuëller, G.I. (eds) Nonlinear Stochastic Dynamic Engineering Systems. IUTAM Symposium. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83334-2_15

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  • DOI: https://doi.org/10.1007/978-3-642-83334-2_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83336-6

  • Online ISBN: 978-3-642-83334-2

  • eBook Packages: Springer Book Archive

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