Pith. sign in

REVIEW 3 major objections 4 minor 56 references

A minimal physical model of cochlear mechanics: Insights into active nonlinear feedback

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that a minimal chain of damped oscillators with exponential, displacement-dependent active feedback can reproduce the cochlea's level-dependent amplification, compressive nonlinearity, frequency selectivity…

desk verdict Useful minimal model of cochlear nonlinearity, but the numerical scheme is under-specified and the quantitative claims are not yet reproducible. read the letter →

arxiv 2608.08096 v1 pith:OB7JIO7P submitted 2026-08-08 physics.bio-ph

Vidyunmathi N. A. , Toby Joseph This is my paper · ORCID
classification physics.bio-ph
keywords cochlearmechanicsactiveprocessbasilarmembranenonlinearfeedbackexponentialdampingtravelingwavecompressivenonlinearityfrequencyselectivity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that a deliberately small model of the cochlea — a one-dimensional chain of damped oscillators, each carrying an exponential, displacement-dependent active feedback term $\beta e^{-(\eta/\eta_{\mathrm{th}})^2}\dot{\eta}$ that mimics outer-hair-cell force generation — can reproduce the main nonlinear signatures of mammalian hearing. Because the active term is strongest at small displacements and fades as displacement grows, weak sounds are amplified, intense sounds grow compressively, and the response stays sharply tuned over a wide range of levels. Coupled through the cochlear fluid and through nearest-neighbor elastic and dissipative interactions, the chain produces traveling waves with realistic frequency-place mapping, Q10 values, gain curves, gain-bandwidth behavior, and roughly 2.5 cycles of phase accumulation at the characteristic frequency. The paper further claims that the higher-order terms contained in the exponential feedback, beyond the cubic approximation used in many active-oscillator models, are needed above about 60 dB SPL to reproduce the gradual transition toward passive mechanics and the partial recovery of linear growth.

What carries the argument

The load-bearing object is the displacement-dependent active damping term in the oscillator equation, $\beta e^{-(\eta/\eta_{\mathrm{th}})^2}\dot{\eta}$, which represents outer-hair-cell feedback opposing viscous damping most strongly at small basilar-membrane displacements. Around $\beta = \gamma$ the local element undergoes a supercritical Hopf bifurcation, so the chain operates close to criticality, and for weak responses the exponential reduces to the familiar cubic nonlinearity of Van der Pol and Rayleigh-type cochlear oscillator models. The distributed model then couples these oscillators through the cochlear fluid via the pressure-displacement relation $\frac{2\rho}{H}\ddot{\eta} = \frac{\partial^2 P}{\partial x^2}$, and through longitudinal elastic and dissipative coupling governed by the strengths $\alpha$ and $\alpha'$, yielding the one-dimensional field equation that is solved numerically by the method of lines.

What would settle it

A decisive check would be to measure basilar-membrane velocity slopes and phase at the characteristic-frequency location for stimulus levels above 90 dB SPL: the exponential model predicts a partial recovery of the local slope toward unity and a phase accumulation near 2.5-2.6 cycles, while a cubic-only model predicts continued compression and a more basal traveling-wave peak. If experiments instead show continued monotonic compression without slope recovery, or phase accumulation differing substantially from the predicted value, the assumed instantaneous in-phase exponential feedback is not the mechanism at work.

Watch

Extended reading notes

Core claim

The central claim is that a single physically motivated feedback law, $\beta e^{-(\eta/\eta_{\mathrm{th}})^2}\dot{\eta}$, appended to a forced damped oscillator, is enough to generate the cochlea's hallmark behaviors once the oscillators are distributed tonotopically and coupled through fluid pressure and nearest-neighbor elastic and dissipative interactions. The system operates near a Hopf bifurcation, with the active strength $\beta$ slightly below the damping coefficient $\gamma$, so small displacements receive nearly complete compensation of damping while larger displacements progressively lose that boost. In the resulting chain, a traveling wave peaks at the place where the local resonant frequency matches the stimulus, the response at that place grows linearly at low levels and compressively at high levels, and phase accumulates steeply near the characteristic place, reaching about 2.5-2.6 cycles. Comparison with a cubic truncation shows nearly identical behavior up to about 60 dB SPL, after which the cubic model over-suppresses gain, keeps compressing, and shifts the traveling-wave peak basally, while the full exponential model retains a sharper peak and recovers toward passive linear response. Longitudinal coupling broadens the frequency response, lowers peak gain, delays the onset of compression, and increases phase accumulation.

Load-bearing premise

The load-bearing premise is that the active feedback force acts instantaneously and exactly in phase with membrane velocity through the term $\beta e^{-(\eta/\eta_{\mathrm{th}})^2}\dot{\eta}$, with no delay; the model's phase accumulation, gain, and high-level behavior all depend on this phase relation, and the authors note that a real active process would generally involve some delay.

Editorial extensions

If this is right

  • If the exponential feedback law is right, a single active term accounts for level-dependent amplification, compressive growth, and frequency selectivity without a separate saturating mechanism.
  • The model predicts Q10 values broadly in line with chinchilla basilar-membrane measurements for target response levels from 25 to 400 micrometers per second.
  • Higher-order nonlinearities beyond the cubic approximation become essential above about 60 dB SPL; cubic-only models mispredict high-level gain, slope recovery, and the location of the traveling-wave peak.
  • Longitudinal elastic and dissipative coupling broadens tuning, reduces low-level gain, delays the onset of compression, and increases accumulated phase; its influence shrinks as stimulus level rises.
  • At the characteristic frequency the model produces roughly 2.5-2.6 cycles of phase accumulation and a level-dependent lead-lag reversal around the CF.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, a sharp experimental test of the exponential-versus-cubic distinction would be to measure basilar-membrane input-output slopes above 90 dB SPL: the exponential model predicts a partial recovery toward linear growth, while the cubic model predicts continued compression.
  • The paper's own suggested extension of adding a phase lag to the active force is the most direct path to fixing its quantitative underestimate of low-level amplification; a small delay would change phase and gain predictions without altering the qualitative framework.
  • Because the feedback is displacement-based rather than velocity-based, responses to transient or chirp stimuli, where displacement and velocity envelopes differ, would discriminate this law from velocity-dependent alternatives more sharply than steady-tone gain curves.
  • Extending the model to two dimensions, as the paper notes, is the most likely way to address the missed high-frequency, high-level basilar-membrane response; the one-dimensional approximation the authors use is known to fail when the excitation wavelength is not small compared to the chamber height.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript proposes a one-dimensional cochlear model in which each longitudinal segment is a damped, driven oscillator with a displacement-dependent exponential active feedback term, coupled through the fluid pressure field and through elastic and dissipative longitudinal interactions. The authors solve the coupled system numerically, compare the exponential feedback with a cubic approximation, and study the effect of longitudinal coupling. They report level-dependent compression, traveling-wave propagation, phase accumulation of roughly 2.6 cycles, Q10 values in the experimental range, and level-dependent gain curves at the characteristic frequency. The Discussion candidly lists three quantitative discrepancies with chinchilla data and proposes extensions including feedback delay and a two-dimensional geometry.

Significance. If the numerical results are reliable, the paper is a useful minimal demonstration that a single exponential displacement-modulated velocity-feedback law, combined with fluid and longitudinal coupling, produces several hallmark cochlear nonlinearities without invoking separate nonlinear feedback laws. The systematic comparison between exponential and cubic nonlinearities and the clean separation of the role of longitudinal coupling are valuable, and the authors deserve credit for explicitly cataloging the model's remaining discrepancies rather than overstating agreement. The main limitation is that the central claims are entirely numerical, while the numerical procedure is not specified at the level needed to verify them and no code or convergence analysis is provided. The significance is therefore conditional on the numerical implementation being made precise and reproducible.

major comments (3)
  1. [Numerical Implementation, Eqs. (2)–(3)] The numerical scheme as described is not a well-posed discretization of the coupled system. Equation (3), ∂²P/∂x² = (2ρ/H)η¨, is an elliptic constraint that must be solved together with Eq. (2) at each instant; stating that 'at each time step, the pressure field was obtained from the discretized fluid equation and subsequently used to evaluate the acceleration' suggests an explicit staggered update that does not enforce the constraint simultaneously. The reported phase accumulation, compressive gain curves, and Q10 values are entirely numerical, so the paper must supply the semi-discrete equations, the time integrator, the treatment of both pressure boundary conditions, the steady-state criterion, and convergence tests in N_x and the time step, or make the code available. Without this information the results cannot be attributed to the continuum model.
  2. [Table 1 and Numerical Implementation] The base frequency ω_b in ω0(x)=ω_b exp(-μx) is not tabulated, even though it determines the location of CF=10 kHz and therefore all frequency-place and Q10 comparisons. In addition, the 30 dB middle-ear gain is mentioned in the text but omitted from Table 1, and it is unclear whether the dB SPL values in Figs. 2–4 refer to ear-canal sound pressure before or after this gain. These omissions make the simulations impossible to reproduce independently.
  3. [Discussion, first paragraph and extension (i)] The active feedback is assumed to be instantaneous and exactly in phase with velocity, and the Discussion acknowledges that real feedback will generally have a delay. Because the phase accumulation and the level-dependent lead-lag reversal in Fig. 5 are direct consequences of this phase relation, the claim that the model 'captures the observed phase behavior' is contingent on the no-delay assumption. The authors should either report a sensitivity test with a small phase lag or explicitly qualify the phase claim in the Results and Summary.
minor comments (4)
  1. [Results, Phase] The phase accumulation is reported as approximately 2.5 cycles in the Results and 2.6 cycles in the Discussion; please make these numbers consistent and specify the stimulus level and frequency at which the value is evaluated.
  2. [Figures 2 and 8] The axis labels appear garbled in the rendering (for example, '7 m/sec' and '#10-7'); please check the fonts, units, and exponent formatting.
  3. [Summary and Discussion] The Summary states that the model 'captures the gain curve at the CF,' but the Discussion lists as discrepancy (iii) a fivefold underestimate of the low-level CF response. Please soften the Summary claim to 'qualitative form of the gain curve' or otherwise add the qualification.
  4. [Numerical Implementation] The text says the first oscillator at the base was fixed, η(0,t)=0, but Eq. (4) contains second spatial derivatives; please specify the finite-difference stencils used at both boundaries so that the discretization of the longitudinal coupling is unambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the model's outputs are emergent from its stated equations and are compared with independent experimental data.

full rationale

The derivation chain is self-contained with respect to its central claims. The active feedback law beta exp(-(eta/eta_th)^2) eta_dot and all parameters in Table 1 are model inputs; the claimed outputs—traveling-wave peak location, level-dependent slope, Q10 values, phase accumulation, and the exponential-versus-cubic differences—are computed from the coupled system (2)-(4), not read off from the inputs. The tonotopic map is explicitly prescribed via omega0(x)=omega_b exp(-mu x), so a peak near the matching CF is an expected consequence, and the paper does not present tonotopy as an emergent prediction. Q10 comparisons are made against independent chinchilla measurements (Ruggero et al. 1997, Rhode 2007), and the Discussion explicitly states that parameters were chosen from general physical considerations rather than fitted to those data, while also acknowledging residual discrepancies such as the fivefold underestimation of low-level gain. The exponential-vs-cubic comparison follows from the chosen functional form, but the quantitative high-level consequences (peak shift, slope recovery, gain degradation) are emergent numerical results. No load-bearing result is justified by a self-citation: the cited prior work, including [21,22,31,32], is external and not by the present authors. The numerical-implementation concern about the Method of Lines is a reproducibility and verification issue, not a circularity of the kind where a prediction equals its input by construction. Therefore no circular step can be quoted.

Assumptions & free parameters 5 free parameters · 3 assumptions · 0 invented entities

The model's central claims rest on the two main assumptions listed above, the active feedback law and the one-dimensional fluid coupling, plus a small set of hand-chosen parameters in Table 1. No new physical entities are introduced. The paper's own Discussion flags the feedback delay and the one-dimensional approximation as limitations.

free parameters (5)
  • Active feedback strength beta = 0.99 gamma = 11880 s^-1
    Set just below the Hopf threshold to provide high sensitivity and compression; no direct measurement of OHC feedback strength is cited.
  • Displacement threshold eta_th = 8 x 10^-7 cm
    Sets the displacement scale at which active feedback weakens; chosen to match basilar-membrane displacement scales and controls the onset of compression.
  • Elastic longitudinal coupling alpha = 3.0 x 10^-4 g cm^2 s^-2
    Chosen to produce broadening of the frequency response; no direct experimental value is cited.
  • Dissipative longitudinal coupling alpha' = 1.2 x 10^-9 g cm^2 s^-1
    Chosen to suppress short-wavelength spatial oscillations; no direct experimental value is cited.
  • Middle ear gain = 30 dB
    Global scaling applied to the stimulus pressure to account for middle-ear transfer; it affects all absolute gain values.
assumptions (3)
  • domain assumption Active OHC feedback is represented as instantaneous displacement-dependent negative damping, beta exp(-(eta/eta_th)^2) eta_dot, in phase with velocity.
    This is the central feedback law of the model (Eq. 1), introduced to mimic OHC activity; it is not derived from OHC biophysics. The authors acknowledge in the Discussion that real feedback may have delay.
  • domain assumption Cochlear fluid is incompressible and inviscid, and the pressure difference obeys the one-dimensional relation 2 rho / H eta_ddot = d^2 P / dx^2.
    Eq. 3 is the fluid coupling that generates traveling waves. The authors note in the Discussion that the one-dimensional approximation fails for various input conditions.
  • domain assumption Tonotopic organization is prescribed by omega_0(x) = omega_b exp(-mu x) with constant mass and exponentially decreasing stiffness.
    The frequency-place map is an input from cochlear physiology, not derived within the model.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A minimal physical model of cochlear mechanics: Insights into active nonlinear feedback." pith.science (2026). https://pith.science/paper/OB7JIO7P

@misc{pith2026260808096,
  author       = {Pith},
  title        = {Pith review of: A minimal physical model of cochlear mechanics: Insights into active nonlinear feedback},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OB7JIO7P}},
  note         = {Machine review of arXiv:2608.08096}
}
read the original abstract

The remarkable sensitivity, compressive nonlinearity, and frequency selectivity of the mammalian cochlea arise from an active process that amplifies the passive mechanical response of the basilar membrane. Outer hair cells are widely regarded as the primary effectors of this active process in the basal regions of the cochlea. This active contribution progressively decreases with increasing stimulus level. Motivated by these observations, a minimal cochlear model is investigated in which each location is represented by a forced damped oscillator with an exponential displacement-dependent active feedback. The oscillators are coupled through the cochlear fluid and also by elastic and dissipative longitudinal interactions to form a one-dimensional distributed model. The model reproduces key features of cochlear mechanics, including level-dependent amplification, compressive nonlinearity, frequency selectivity, traveling-wave propagation, and phase accumulation. Comparison with a simplified cubic nonlinear model has been carried out. Even though the cubic nonlinearity describes the response for weak stimuli, at higher stimulus levels it deviates from the exponential model and fails to reproduce the gradual transition towards predominantly passive behavior. Longitudinal coupling broadens the frequency response, modifies the traveling wave profile, and increases phase accumulation. The proposed model provides a simple physical framework for understanding how local active processes and longitudinal mechanical interactions together shape the nonlinear response of the cochlea.

Figures

Figures reproduced from arXiv: 2608.08096 by the authors.

Figure 1
Figure 1. Spatial displacement profiles of the traveling wave for 20 kHz [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Model response illustrating level-dependent nonlinear compression [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Model-predicted iso-response tuning curves. The lowest threshold [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Frequency selectivity characteristics of the model at stimulus levels [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Phase accumulation as a function of stimulus frequency at differ [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Comparison between the exponential and cubic nonlinear models. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Comparison of the exponential model with ( [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: Traveling-wave profiles at 20 dB SPL and 90 dB SPL for (a) [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 2
Figure 2. Figure 2: The compressed growth of the response enables the ear to process [PITH_FULL_IMAGE:figures/full_fig_p018_2.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages

  1. [1]

    Neuron , volume=

    How hearing happens , author=. Neuron , volume=. 1997 , publisher=

    work page 1997

  2. [2]

    1989 , publisher=

    Mechanics of hearing , author=. 1989 , publisher=

    work page 1989

  3. [3]

    The transformation of sound stimuli into electrical signals , language =

    Fettiplace, Robert , file =. The transformation of sound stimuli into electrical signals , language =

    work page

  4. [4]

    Olson , keywords =

    Elizabeth S. Olson , keywords =. 2.21 - Mechanics of the Cochlea , editor =. The Senses: A Comprehensive Reference (Second Edition) , publisher =. 2020 , isbn =. doi:https://doi.org/10.1016/B978-0-12-809324-5.24124-2 , url =

    work page doi:10.1016/b978-0-12-809324-5.24124-2 2020

  5. [5]

    Reports on Progress in Physics , volume=

    The physics of hearing: fluid mechanics and the active process of the inner ear , author=. Reports on Progress in Physics , volume=. 2014 , publisher=

    work page 2014

  6. [6]

    Journal of neurophysiology , volume=

    A critique of the critical cochlea: Hopf—a bifurcation—is better than none , author=. Journal of neurophysiology , volume=. 2010 , publisher=

    work page 2010

  7. [7]

    Physiological reviews , volume=

    Mechanics of the mammalian cochlea , author=. Physiological reviews , volume=. 2001 , publisher=

    work page 2001

  8. [8]

    The journal of neuroscience , volume=

    The active cochlea , author=. The journal of neuroscience , volume=. 1992 , publisher=

    work page 1992

Show all 56 references
  1. [9]

    Annual Review of Condensed Matter Physics , volume=

    Mechanical frequency tuning by sensory hair cells, the receptors and amplifiers of the inner ear , author=. Annual Review of Condensed Matter Physics , volume=. 2021 , publisher=

    2021

  2. [10]

    Nature Reviews Neuroscience , volume=

    Integrating the active process of hair cells with cochlear function , author=. Nature Reviews Neuroscience , volume=. 2014 , publisher=

    2014

  3. [11]

    1997 , publisher=

    How hearing happens , journal=. 1997 , publisher=

    1997

  4. [12]

    2008 , publisher=

    Making an Effort to Listen: Mechanical Amplification in the Ear , journal=. 2008 , publisher=

    2008

  5. [13]

    Cell and tissue research , volume=

    Basic response properties of auditory nerve fibers: a review , author=. Cell and tissue research , volume=. 2015 , publisher=

    2015

  6. [14]

    Nature , volume=

    The postsynaptic function of type II cochlear afferents , author=. Nature , volume=. 2009 , publisher=

    2009

  7. [15]

    Journal of Neuroscience , volume=

    Excitability of type II cochlear afferents , author=. Journal of Neuroscience , volume=. 2014 , publisher=

    2014

  8. [16]

    The Journal of Physiology , volume=

    Encoding sound in the cochlea: from receptor potential to afferent discharge , author=. The Journal of Physiology , volume=. 2021 , publisher=

    2021

  9. [17]

    Hearing research , volume=

    Volume gradients in inner hair cell-auditory nerve fiber pre-and postsynaptic proteins differ across mouse strains , author=. Hearing research , volume=. 2020 , publisher=

    2020

  10. [18]

    The Journal of the Acoustical Society of America , volume=

    The interplay between active hair bundle motility and electromotility in the cochlea , author=. The Journal of the Acoustical Society of America , volume=. 2010 , publisher=

    2010

  11. [19]

    International journal of biomedical science: IJBS , volume=

    The efferent system or olivocochlear function bundle--fine regulator and protector of hearing perception , author=. International journal of biomedical science: IJBS , volume=. 2010 , publisher=

    2010

  12. [20]

    Auditory Efferent System; A Review on Anatomical Structure and Functional Bases , volume =

    Javanbakht, Mohanna , year =. Auditory Efferent System; A Review on Anatomical Structure and Functional Bases , volume =. Global Journal of Otolaryngology , doi =

  13. [21]

    Cold Spring Harbor Perspectives in Medicine , volume=

    Hair cell afferent synapses: function and dysfunction , author=. Cold Spring Harbor Perspectives in Medicine , volume=. 2019 , publisher=

    2019

  14. [22]

    2008 , file =

    Active processes and otoacoustic emissions in hearing , isbn =. 2008 , file =

    2008

  15. [23]

    1982 , publisher=

    The Senses , author=. 1982 , publisher=

    1982

  16. [24]

    The Journal of the Acoustical Society of America , volume=

    Basilar membrane mechanics in the 6--9kHz region of sensitive chinchilla cochleae , author=. The Journal of the Acoustical Society of America , volume=. 2007 , publisher=

    2007

  17. [25]

    The Journal of the Acoustical Society of America , volume=

    Basilar-membrane responses to tones at the base of the chinchilla cochlea , author=. The Journal of the Acoustical Society of America , volume=. 1997 , publisher=

    1997

  18. [26]

    arXiv preprint arXiv:2512.11646 , year=

    Marrying critical oscillators with traveling waves shapes nonlinear sound processing in the cochlea , author=. arXiv preprint arXiv:2512.11646 , year=

  19. [27]

    2024 , school=

    Marrying the physics of critical oscillators with traveling-wave models of the cochlea , author=. 2024 , school=

    2024

  20. [28]

    Active Traveling Wave in the Cochlea , author =. Phys. Rev. Lett. , volume =. 2003 , month =. doi:10.1103/PhysRevLett.90.158101 , url =

    2003 doi

  21. [29]

    1964 , institution=

    An SU \_3 model for strong interaction symmetry and its breaking , author=. 1964 , institution=

    1964

  22. [30]

    Cold Spring Harbor symposia on quantitative biology , volume=

    Basilar membrane motion , author=. Cold Spring Harbor symposia on quantitative biology , volume=. 1976 , organization=

    1976

  23. [31]

    Allen, J. B. , title =. The Journal of the Acoustical Society of America , volume =. 1977 , month =. doi:10.1121/1.381272 , url =

    1977 doi

  24. [32]

    and Taber, Larry A

    Steele, Charles R. and Taber, Larry A. , title =. The Journal of the Acoustical Society of America , volume =. 1979 , month =. doi:10.1121/1.382570 , url =

    1979 doi

  25. [33]

    The Journal of the Acoustical Society of America , volume=

    Mathematical modeling of cochlear mechanics , author=. The Journal of the Acoustical Society of America , volume=. 1985 , publisher=

    1985

  26. [34]

    Biophysics of the cochlea: Linear approximation , volume =

    Nobili, Renato and Mammano, Fabio , year =. Biophysics of the cochlea: Linear approximation , volume =

  27. [35]

    and Mammano, F

    Nobili, R. and Mammano, F. , title =. The Journal of the Acoustical Society of America , volume =. 1996 , month =. doi:10.1121/1.415412 , url =

    1996 doi

  28. [36]

    Essential Nonlinearities in Hearing , author =. Phys. Rev. Lett. , volume =. 2000 , month =. doi:10.1103/PhysRevLett.84.5232 , url =

    2000 doi

  29. [37]

    A Wave Traveling over a Hopf Instability Shapes the Cochlear Tuning Curve , author =. Phys. Rev. Lett. , volume =. 2003 , month =. doi:10.1103/PhysRevLett.90.058101 , url =

    2003 doi

  30. [38]

    Békésy, Georg , title =

    v. Békésy, Georg , title =. The Journal of the Acoustical Society of America , volume =. 1949 , month =. doi:10.1121/1.1906503 , url =

    1949 doi

  31. [39]

    Olson and Hendrikus Duifhuis and Charles R

    Elizabeth S. Olson and Hendrikus Duifhuis and Charles R. Steele , abstract =. Von Békésy and cochlear mechanics , journal =. 2012 , note =. doi:https://doi.org/10.1016/j.heares.2012.04.017 , url =

    2012 doi

  32. [40]

    Observations of the vibration of the basilar membrane in squirrel monkeys using the M

    Rhode, William S , journal=. Observations of the vibration of the basilar membrane in squirrel monkeys using the M. 1971 , publisher=

    1971

  33. [41]

    The Journal of the Acoustical Society of America , volume=

    Stimulated acoustic emissions from within the human auditory system , author=. The Journal of the Acoustical Society of America , volume=. 1978 , publisher=

    1978

  34. [42]

    Proceedings of the National Academy of Sciences , volume =

    Sébastien Camalet and Thomas Duke and Frank Jülicher and Jacques Prost , title =. Proceedings of the National Academy of Sciences , volume =. 2000 , doi =. https://www.pnas.org/doi/pdf/10.1073/pnas.97.7.3183 , abstract =

    doi

  35. [43]

    AIP Conference Proceedings , volume=

    Hopf-Bifurcations and Van der Pol Oscillator Models of the Mammalian Cochlea , author=. AIP Conference Proceedings , volume=. 2011 , organization=

    2011

  36. [44]

    Mechanics of Hearing: Proceedings of the IUTAM/ICA Symposium Held at Delft University of Technology The Netherlands 13--15 July 1983 , pages=

    Department of Mathematics and Informatics Delft University of Technology, The Netherlands , author=. Mechanics of Hearing: Proceedings of the IUTAM/ICA Symposium Held at Delft University of Technology The Netherlands 13--15 July 1983 , pages=. 1983 , organization=

    1983

  37. [45]

    The Journal of the Acoustical Society of America , volume=

    Nonlinear and active two-dimensional cochlear models: Time-domain solution , author=. The Journal of the Acoustical Society of America , volume=. 1989 , publisher=

    1989

  38. [46]

    Peripheral Auditory Mechanisms: Proceedings of a conference held at Boston University, Boston, MA, August 13--16, 1985 , pages=

    Modelling the cochlear partition with coupled Van der Pol oscillators , author=. Peripheral Auditory Mechanisms: Proceedings of a conference held at Boston University, Boston, MA, August 13--16, 1985 , pages=. 1986 , organization=

    1985

  39. [47]

    2012 , publisher=

    Cochlear mechanics: Introduction to a time domain analysis of the nonlinear cochlea , author=. 2012 , publisher=

    2012

  40. [48]

    The Mechanics and Biophysics of Hearing: Proceedings of a Conference held at the University of Wisconsin, Madison, WI, June 25--29, 1990 , pages=

    A generalized Van der Pol-oscillator cochlea model , author=. The Mechanics and Biophysics of Hearing: Proceedings of a Conference held at the University of Wisconsin, Madison, WI, June 25--29, 1990 , pages=. 1990 , organization=

    1990

  41. [49]

    , author=

    Morphometry of the chinchilla organ of Corti and stria vascularis. , author=. Journal of Histochemistry & Cytochemistry , volume=. 1979 , publisher=

    1979

  42. [50]

    Hearing research , volume=

    A physiological frequency-position map of the chinchilla cochlea , author=. Hearing research , volume=. 2010 , publisher=

    2010

  43. [51]

    Mechanics of Hearing Workshop 2024 , year=

    Nonlinear Tuning from Coupled Critical Oscillators in a Travelling-Wave Model of The Cochlea , author=. Mechanics of Hearing Workshop 2024 , year=

    2024

  44. [52]

    The Journal of the Acoustical Society of America , volume=

    Inner-ear sound pressures near the base of the cochlea in chinchilla: Further investigation , author=. The Journal of the Acoustical Society of America , volume=. 2013 , publisher=

    2013

  45. [53]

    The Journal of the Acoustical Society of America , volume=

    Middle-ear velocity transfer function, cochlear input immittance, and middle-ear efficiency in chinchilla , author=. The Journal of the Acoustical Society of America , volume=. 2013 , publisher=

    2013

  46. [54]

    The Journal of the Acoustical Society of America , volume=

    Middle ear function and cochlear input impedance in chinchilla , author=. The Journal of the Acoustical Society of America , volume=. 2010 , publisher=

    2010

  47. [55]

    Physical Review Letters , volume=

    Essential role of couplings between hearing nonlinearities , author=. Physical Review Letters , volume=. 2003 , publisher=

    2003

  48. [56]

    Nonlinear dynamics of cochlear information processing , author=. Proc. Int. Workshop of Nonlinear Dynamics of Electronic Systems (NDES-04), Evora, Portugal , pages=

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.