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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
9/2005

Self-tuning to the Hopf bifurcation in fluctuating systems

Janaki Balakrishnan

Abstract

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.

Received:
Feb 7, 2005
Published:
Feb 7, 2005
MSC Codes:
82C31, 37N35, 93B52, 60G35, 37N25, 92C05
PACS:
05.40.-a, 02.50.Ey, 05.10.Gg, 05.45.-a, 05.40.Ca, 87.10.+e
Keywords:
fluctuations, fokker-planck equation, hopf bifurcation, adiabatic elimination, nonlinearities

Related publications

inJournal
2005 Repository Open Access
Janaki Balakrishnan

Self-tuning to the Hopf bifurcation in fluctuating systems

In: Journal of physics / A, 38 (2005) 8, pp. 1627-1652