Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nlin/0202004

Time Domain Computation of a Nonlinear Nonlocal Cochlear Model with Applications to Multitone Interaction in Hearing

Jack Xin·Yingyong Qi·Li Deng
View original source ↗Read source document ↗Export metadata ↓

Abstract

A nonlinear nonlocal cochlear model of the transmission line type is studied in order to capture the multitone interactions and resulting tonal suppression effects. The model can serve as a module for voice signal processing, it is a one dimensional (in space) damped dispersive nonlinear PDE based on mechanics and phenomenology of hearing. It describes the motion of basilar membrane (BM) in the cochlea driven by input pressure waves. Both elastic damping and selective longitudinal fluid damping are present. The former is nonlinear and nonlocal in BM displacement, and plays a key role in capturing tonal interactions. The latter is active only near the exit boundary (helicotrema), and is built in to damp out the remaining long waves. The initial boundary value problem is numerically solved with a semi-implicit second order finite difference method. Solutions reach a multi-frequency quasi-steady state. Numerical results are shown on two tone suppression from both high-frequency and low-frequency sides, consistent with known behavior of two tone suppression. Suppression effects among three tones are demonstrated by showing how the response magnitudes of the fixed two tones are reduced as we vary the third tone in frequency and amplitude. We observe qualitative agreement of our model solutions with existing cat auditory neural data. The model is thus simple and efficient as a processing tool for voice signals.

Explore related subjects

nlin.PS

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jack Xin, Yingyong Qi, Li Deng. 2002-09-20. Time Domain Computation of a Nonlinear Nonlocal Cochlear Model with Applications to Multitone Interaction in Hearing. https://doi.org/10.1121/1.4779257

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Hyperbolic-Tangent Shocks in a Lossy Nonlinear Transmission Line

We consider a lossy transmission line with a nonlinear voltage--charge relation. We derive an equation for a traveling front with the charge approaching constant asymptotic values on both sides of the front and solve the inverse problem for this equation exactly. Starting from a prescribed monotonic front profile and a prescribed front speed, we determine the dimensionless squared local sound speed within the front. This quantity is the central object of our analysis and allows us to determine the voltage--charge relation of the transmission line in which the front propagates. The squared sound speed, averaged uniformly over the charge interval spanned by the front, is equal to the squared front speed. We specifically consider fronts with a hyperbolic-tangent profile. All physically admissible fronts of this form are shocks rather than kinks. The voltage--charge relation of the transmission line in which the shock propagates is expressed in terms of the lower incomplete beta function. We also treat a transmission line with a cubic voltage--charge relation and propose an approximate equation that admits the hyperbolic-tangent shock profile as an exact solution. The results of the approximate approach coincide with the broad-shock approximation of the exact inverse solution.

nlin.PS↗
arXiv2026

Deformation of sine-Gordon two-soliton solutions in $φ^4$ kink-antikink configurations

In this work, we construct analytical kink-antikink $(K\bar{K})$ configurations in the non-integrable $φ^4$ model by mapping exact solutions of the integrable sine-Gordon system via a field deformation. This procedure yields two distinct classes of configurations, parametrized by the initial half-separation and velocity. We compare these profiles with the standard additive superposition Ansatz in terms of vacuum structure and equation-of-motion residuals, deriving explicit closed-form expressions for the corresponding integrated squared residuals. For small separations, the mapped soliton-antisoliton configurations exhibit appreciably smaller residuals than the naive superposition Ansatz, which in turn performs better than the mapped two-soliton configurations. Although the mapped fields are not exact solutions of the $φ^4$ equation of motion, they provide mathematically consistent, topologically sound, and physically motivated initial data for numerical studies of kink-antikink scattering and resonance phenomena.

nlin.PS↗
arXiv2026

Extreme Events in an Active Fluid Medium

We observe the emergence of extreme events in an active fluid involving two distinct chemical species that regulate active stress. One species is slow diffusing and the other is fast diffusing, and the growth of the fast-diffusing species is modelled using a nonlinear logistic term. We demonstrate the presence of extreme events in the temporal evolution of the concentrations, as well as in the spatial profile of the system,in regimes of merging-emerging soliton-like dynamics and spatio-temporal chaos, through analysis of the time-series, bifurcation diagrams, probability distribution functions of the concentration of the two species, return maps and distributions of inter-event intervals. Interestingly, we also find evidence of pronounced bunching of extreme events and super-extreme events in the slow chemical species in the soliton-like regime. We go on to systematically explore the dependence of the extreme event occurrences on the Péclet number and the strength of the nonlinear growth term, and find that the probability of extreme events increases after a critical Péclet number, while increasing the nonlinearity suppresses extreme events. Lastly, in order to gain further insight, we investigate a modified mode-truncated reduced order model comprising of coupled differential equations mimicking this active fluid system. We find that this reduced order model also exhibits extreme events whose emergence is correlated with a sudden expansion in attractor size due to a crisis arising from attractor collision.So these results demonstrate the existence of extreme events in an active fluid system, and are of potential relevance to biological phenomena where active transport plays an important role.

nlin.PS↗