Abstract
Many cochlear models describe the basilar membrane as a distributed transmission line, while others interpret active auditory mechanics through nonlinear oscillators near a Hopf bifurcation. This work connects these views analytically by showing that the local dynamics of the transmission-line formulation can be reduced to a Stuart–Landau oscillator near the bifurcation point.
A numerical simulation framework then demonstrates how an ensemble of coupled oscillators reproduces cochlear features such as sharp tuning at low levels, compressive nonlinearities, and traveling-wave-like behavior across the tonotopic axis.
Highlights
- Analytical reduction from a transmission-line element to Hopf normal form
- Interpretation of cochlear partition dynamics as coupled Stuart–Landau oscillators
- Numerical simulations of 600 oscillators from 200 Hz to 16 kHz
- Frequency selectivity and level-dependent compression
- Traveling-wave-like dynamics emerging across the oscillator array
Video
Animation of the basilar membrane displacement in response to a 1 kHz sinusoidal stimulus with a group of coupled SLOs. A traveling wave progresses from the base to the apex across the oscillator ensemble.
Method
The paper derives Hopf conditions for a local transmission-line element with delayed feedback, shows the existence of a bifurcation, and then reduces the local dynamics to a complex Stuart–Landau equation on the center manifold.
Simulations are performed for coupled oscillators with nearest-neighbor interactions, allowing comparison between a transmission-line viewpoint and a coupled-oscillator description of cochlear mechanics.
Results
The simulations show strong frequency selectivity at low stimulus levels, a shift of the peak response toward lower characteristic frequencies at higher levels, and compressive nonlinear behavior. The transient dynamics also exhibit a traveling-wave-like pattern along the oscillator array.
These observations support the interpretation that coupled Hopf-type oscillators provide a compact and insightful model for cochlear partition dynamics near the bifurcation regime.