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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/192

Title: Controlling stochastic oscillations close to a Hopf bifurcation by time-delayed feedback
Authors: Scholl, E.
Balanov, Alexander G.
Janson, Natalia B.
Neiman, A.
Keywords: mathematics
stochastic delay-differential equations
noise-induced oscillations
Issue Date: 2004
Abstract: We study the effect of a time-delayed feedback upon a Van der Pol oscillator under the influence of white noise in the regime below the Hopf bifurcation where the deterministic system has a stable fixed point. We show that both the coherence and the frequency of the noise-induced oscillations can be controlled by varying the delay time and the strength of the control force. Approximate analytical expressions for the power spectral density and the coherence properties of the stochastic delay differential equation are developed, and are in good agreement with our numerical simulations. Our analytical results elucidate how the correlation time of the controlled stochastic oscillations can be maximized as a function of delay and feedback strength.
Description: This is a pre-print.
URI: https://dspace.lboro.ac.uk/2134/192
Appears in Collections:Pre-prints (Maths)

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