arXiv subjects

Yuval Edri

Publications and source records attributed to Yuval Edri.

4 recordsLinked to original sources

arXiv2019

Spatial asymmetries of resonant oscillations in periodically forced heterogeneous media

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.

nlin.PS↗

arXiv2019

Spatial heterogeneity may form an inverse camel shape Arnol'd tongue in parametrically forced oscillations

Frequency locking in forced oscillatory systems typically occurs in 'V'-shaped domains in the plane spanned by the forcing frequency and amplitude, the so-called Arnol'd tongues. Here, we show that if the medium is spatially extended and monotonically heterogeneous, e.g., through spatially-dependent natural frequency, the resonance tongues can also display 'U' and 'W' shapes; to the latter, we refer as "inverse camel" shape. We study the generic forced complex Ginzburg-Landau equation for damped oscillations under parametric forcing and, using linear stability analysis and numerical simulations, uncover the mechanisms that lead to these distinct shapes. Additionally, we study the effects of discretization, by exploring frequency locking of oscillators chains. Since we study a normal-form equation, the results are model-independent near the onset of oscillations, and, therefore, applicable to inherently heterogeneous systems in general, such as the cochlea. The results are also applicable to controlling technological performances in various contexts, such as arrays of mechanical resonators, catalytic surface reactions, and nonlinear optics.

nlin.PS↗

arXiv2018

Molding the asymmetry of localized frequency-locking waves by a generalized forcing and implications to the inner ear

Frequency locking to an external forcing frequency is a {well} known phenomenon. In the auditory system, it results in a localized traveling wave, the shape of which is essential for efficient discrimination between incoming frequencies. An amplitude equation approach is used to show that the shape of the localized traveling wave depends crucially on the relative strength of additive vs. parametric forcing components; the stronger the parametric forcing the more asymmetric the response profile and the sharper the traveling-wave front. The analysis captures the empirically observed regions of linear and nonlinear responses and highlights the significance of parametric forcing mechanisms in shaping the resonant response in the inner ear.

nlin.PS↗

arXiv2016

Frequency locking in auditory hair cells: Distinguishing between additive and parametric forcing

The auditory system displays remarkable sensitivity and frequency discrimination, attributes shown to rely on an amplification process that involves a mechanical as well as a biochemical response. Models that display proximity to an oscillatory onset (a.k.a. Hopf bifurcation) exhibit a resonant response to distinct frequencies of incoming sound, and can explain many features of the amplification phenomenology. To understand the dynamics of this resonance, frequency locking is examined in a system near the Hopf bifurcation and subject to two types of driving forces: additive and parametric. Derivation of a universal amplitude equation that contains both forcing terms enables a study of their relative impact on the hair cell response. In the parametric case, although the resonant solutions are 1:1 frequency locked, they show the coexistence of solutions obeying a phase shift of $\pi$, a feature typical of the 2:1 resonance. Different characteristics are predicted for the transition from unlocked to locked solutions, leading to smooth or abrupt dynamics in response to different types of forcing. The theoretical framework provides a more realistic model of the auditory system, which incorporates a direct modulation of the internal control parameter by an applied drive. The results presented here can be generalized to many other media, including Faraday waves, chemical reactions, and nonlinear optics, which are known to exhibit resonant behavior.

nlin.PS↗