Self-tuning to the Hopf bifurcation in fluctuating systems
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Submission date: 07. Feb. 2005
published in: Journal of physics / A, 38 (2005) 8, p. 1627-1652
DOI number (of the published article): 10.1088/0305-4470/38/8/001
MSC-Numbers: 82C31, 37N35, 93B52, 60G35, 37N25, 92C05
PACS-Numbers: 05.40.-a, 02.50.Ey, 05.10.Gg, 05.45.-a, 05.40.Ca, 87.10.+e
Keywords and phrases: fluctuations, fokker-planck equation, hopf bifurcation, adiabatic elimination, nonlinearities
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The problem of self-tuning a system to the Hopf bifurcation in the presence of noise and periodic external forcing is discussed. We find that the response of the system has a non-monotonic dependence on the noise-strength, and displays an amplified response which is more pronounced for weaker signals. The observed effect is to be distinguished from stochastic resonance. For the feedback we have studied, the unforced self-tuned Hopf oscillator in the presence of fluctuations exhibits sharp peaks in its spectrum. The implications of our general results are briefly discussed in the context of sound detection by the inner ear.