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Dynamics of the moment equations of a stochastic Duffing oscillator. (English) Zbl 0983.70538

Spanos, P. D. (ed.), Computational stochastic mechanics. Proceedings of the 3rd international conference (CSM’98) held on Santorini, Greece, June 14-17, 1998. Rotterdam: A. A. Balkema. 143-148 (1999).
Summary: Statistical moments of response are widely used in the analysis of stochastic dynamical systems of engineering interest. It is known that, if the inputs to the system are Gaussian or filtered Gaussian white noise, ItĂ´’s rule can be used to generate a system of first-order linear differential equations governing the evolution of the response moments. For nonlinear systems, the moment equations form an infinite hierarchy, necessitating the application of a closure procedure to truncate the system at some finite dimensions at the expense of making the moment equations nonlinear. The simplest of these schemes is termed Gaussian closure. Here, the response of the dynamical system is assumed to be Gaussian, as is the case for a linear system; consequently, the response of the system is completely characterized by its first- and second-order moments. It is well known that the resulting closed system of nonlinear equations can possess rich dynamics, thus motivating further investigations.
For the entire collection see [Zbl 0929.00080].

MSC:

70L05 Random vibrations in mechanics of particles and systems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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