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Modelling and simulation of autonomous oscillators with random parameters

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  • Pulch, Roland

Abstract

We consider periodic problems of autonomous systems of ordinary differential equations or differential algebraic equations. To quantify uncertainties of physical parameters, we introduce random variables in the systems. Phase conditions are required to compute the resulting periodic random process. It follows that the variance of the process depends on the choice of the phase condition. We derive a necessary condition for a random process with a minimal total variance by the calculus of variations. A corresponding numerical method is constructed based on the generalised polynomial chaos. We present numerical simulations of two test examples.

Suggested Citation

  • Pulch, Roland, 2011. "Modelling and simulation of autonomous oscillators with random parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1128-1143.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:6:p:1128-1143
    DOI: 10.1016/j.matcom.2010.10.028
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    References listed on IDEAS

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    1. Pulch, Roland & van Emmerich, Cathrin, 2009. "Polynomial chaos for simulating random volatilities," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 245-255.
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    Cited by:

    1. Pulch, Roland & ter Maten, E. Jan W. & Augustin, Florian, 2015. "Sensitivity analysis and model order reduction for random linear dynamical systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 111(C), pages 80-95.

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