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Response statistics of van der Pol oscillators excited by white noise

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Abstract

The joint probability density function of the state space vector of a white noise exoited van der Pol oscillator satisfics a Fokker-Planck-Kolmogorov (FPK) equation. The paper describes a numerical procedure for solving the transient FPK equation based on the path integral solution (PIS) technique. It is shown that by combining the PIS with a cubic B-spline interpolation method, numerical solution algorithms can be implemented giving solutions of the FPK equation that can be made accurate down to very low probability levels. The method is illustrated by application to two specific examples of a van der Pol oscillator.

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Authors and Affiliations

  1. Faculty of Civil Engineering, Norwegian Institute of Technology, Rich, Birkelaads vei la, N-7034, Trondheim, Norway

    A. Naess & B. K. Hegstad

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  1. A. Naess
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  2. B. K. Hegstad
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Naess, A., Hegstad, B.K. Response statistics of van der Pol oscillators excited by white noise. Nonlinear Dyn 5, 287–297 (1994). https://doi.org/10.1007/BF00045338

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  • DOI: https://doi.org/10.1007/BF00045338

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