Abstract
In this article an algorithm for the numerical approximation of random attractors based on the subdivision algorithm of Dellnitz and Hohmann is presented. It is applied to the stochastic Duffing-van der Pol oscillator, for which we also prove a theoretical result on the existence of stable/unstable manifolds and attractors. This system serves as a main example for a stochastically perturbed Hopf bifurcation. The results of our computations suggest that the structure of the random Duffing-van der Pol attractor and the dynamics on it are more complicated than assumed previously.
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Keller, H., Ochs, G. (1999). Numerical Approximation of Random Attractors. In: Stochastic Dynamics. Springer, New York, NY. https://doi.org/10.1007/0-387-22655-9_5
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DOI: https://doi.org/10.1007/0-387-22655-9_5
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