Spatial asymmetries of resonant oscillations in periodically forced heterogeneous media
arXiv:1912.12489 · doi:10.1016/j.physd.2020.132501
Abstract
Spatially localized oscillations in periodically forced systems are intriguing phenomena. They may occur in spatially homogeneous media (oscillons), but quite often emerge in heterogeneous media, such as the auditory system, where localized oscillations are believed to play an important role in frequency discrimination of incoming sound waves. In this paper, we use an amplitude-equation approach to study the spatial profile of the oscillations and the factors that affect it. More specifically, we use a variant of the forced complex Ginzburg-Landau (FCGL) equation to describes an oscillatory system below the Hopf bifurcation with space-dependent Hopf frequency, subject to both parametric and additive forcing. We show that spatial heterogeneity, combined with bistability of system states, results in spatial asymmetry of the localized oscillations. We further identify parameters that control that asymmetry, and characterize the spatial profile of the oscillations in terms of maximum amplitude, location, width and asymmetry. Our results bear qualitative similarities to empirical observation trends that have found in the auditory system.
arXiv comment14 pages, 8 figures
References in corpus (16)
- Hexagons, Kinks and Disorder in Oscillated Granular Layers
- Essential nonlinearities in hearing
- Response of parametrically-driven nonlinear coupled oscillators with application to micro- and nanomechanical resonator arrays
- Intrinsic localized modes in parametrically-driven arrays of nonlinear resonators
- Resonance tongues and patterns in periodically forced reaction-diffusion systems
- A ratchet mechanism for amplification in low-frequency mammalian hearing
- Parametrically excited water surface ripples as ensembles of oscillons
- Slanted snaking of localized Faraday waves
- Localized patterns in periodically forced systems
- Nonlinear Oscillations and Bifurcations in Silicon Photonic Microresonators
- Localized Faraday patterns under heterogeneous parametric excitation
- Two-dimensional localized structures in harmonically forced oscillatory systems
- Frequency locking in auditory hair cells: Distinguishing between additive and parametric forcing
- Spatial heterogeneity may form an inverse camel shape Arnol'd tongue in parametrically forced oscillations
- Comb-like Turing patterns embedded in Hopf oscillations: Spatially localized states outside the 2:1 frequency locked region
- Molding the asymmetry of localized frequency-locking waves by a generalized forcing and implications to the inner ear