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Analysis and Simulation of Nonlinear Stochastic Systems

  • Walter V. Wedig
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

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

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    Wedig, W.: Pitchfork and Hopf bifurcations in stochastic systems - effective methods to calculate Lyapunov exponents. To appear in: Effective Stochastic Analysis (ed. by P. Krée, W. Wedig)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Walter V. Wedig
    • 1
  1. 1.Institute for Technical MechanicsUniversity of KarlsruheDeutschland

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