Abstract
We develop a multi-scale analysis for stochastic differential equations. Such models are particularly sensitive to noise when the system is near a critical point, such as a Hopf bifurcation, which marks a transition to oscillatory behavior. In particular, we are interested in the case when the combined effects of the noise and the bifurcation amplify oscillations which would decay in the deterministic system. The derivation of reduced equations for the envelope of the oscillations provides an efficient analysis of the dynamics by separating the influence of the noise from the intrinsic oscillations over long time scales.
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Kuske, R. (2003). Multi-Scale Analysis of Noise-Sensitivity Near a Bifurcation. In: Namachchivaya, N.S., Lin, Y.K. (eds) IUTAM Symposium on Nonlinear Stochastic Dynamics. Solid Mechanics and Its Applications, vol 110. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0179-3_12
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DOI: https://doi.org/10.1007/978-94-010-0179-3_12
Publisher Name: Springer, Dordrecht
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