2005/02/09 by J. Balakrishnan, Janaki Balakrishnan
Biochemistry, Genetics and Molecular Biology · Computer Science · Environmental Science · Physics and Astronomy · #Ecosystem dynamics and resilience #Nonlinear Dynamics and Pattern Formation #cond-mat.stat-mech #nlin.CD #physics.bio-ph #q-bio.QM #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/0305-4470/38/8/001
published as J.Phys.A 38, 1627 (2005) · 37 pages, 7 figures (8 figure files)
arxiv created 2005/02/09 · openalex publication_date 2005/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.