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Local exponents of nonlinear compression in periodically driven noisy oscillators
Benjamin Lindner1, Kai Dierkes, Frank Jülicher
1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Physical Review Letters
|April 7, 2010
Summary
Active amplifiers in the inner ear use nonlinear signal compression. This study analytically calculates the local exponent for a generic oscillator, finding values near -1 for strong compression under specific conditions.
Area of Science:
- Auditory Neuroscience
- Nonlinear Dynamics
- Biophysics
Background:
- Nonlinear signal compression is crucial for active amplification in vertebrate inner ear organs.
- Observed exponents (alpha(0)) for sensitivity versus forcing amplitude range from -0.88 to -0.5.
- Understanding these exponents is key to explaining auditory sensitivity and function.
Purpose of the Study:
- To analytically calculate the local exponent of signal compression for a generic oscillator.
- To investigate the influence of noise and periodic forcing on this exponent.
- To determine conditions under which strong compression (exponent near -1) occurs.
Main Methods:
- Analytical calculation of the local exponent for a normal form oscillator.
- Modeling a Hopf bifurcation with added noise and periodic forcing.
- Analysis of the oscillator's response to varying forcing amplitudes.
Main Results:
- The local exponent was calculated for a generic oscillator model.
- For weak noise and sufficient distance from the bifurcation, the exponent can approach -1.
- This strong compression occurs for moderate forcing amplitudes beyond linear response.
Conclusions:
- The study provides an analytical framework for understanding nonlinear signal compression in active amplifiers.
- The findings suggest that exponents near -1 are achievable under specific conditions, explaining strong compression.
- The results are consistent with models of hair bundle motility, supporting their biological relevance.
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