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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…
It is shown on the basis of the multiplicative renormalization-group method of two-loop order that the low-energy effective Hamiltonian of a strongly coupled local electron-phonon system is mapped to the two-channel Kondo model. A phonon is…
The logistic two-gene negative-feedback oscillator is locally asymptotically stable for all biological parameter values, since the trace of the Jacobian is uniformly negative. Real biological oscillators (circadian rhythms, the segmentation…
In this work we present a data-driven approach for predicting the behavior of (i.e., profiling) a given non-linear audio signal processing effect (henceforth "audio effect"). Our objective is to learn a mapping function that maps the…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
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…
This paper presents a method for modeling optical dynamic range compressors using deep neural networks with Selective State Space models. The proposed approach surpasses previous methods based on recurrent layers by employing a Selective…
In Part I of this paper, we have used spectral submanifold (SSM) theory to construct reduced-order models for harmonically excited mechanical systems with internal resonances. In that setting, extracting forced response curves formed by…
The phenomenon of stochastic resonance, wherein the stimulus-response of a system can be maximized by an intermediate level of noise, has been extensively investigated through linear response theory. As yet a unified response-noise or…
The long-term mean-field dynamics of coupled underdamped Duffing oscillators driven by an external periodic signal with Gaussian noise is investigated. A Boltzmann-type H-theorem is proved for the associated nonlinear Fokker-Planck equation…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
We develop a model of bistable oscillator with nonlinear dissipation. Using a numerical simulation and an electronic circuit realization of this system we study its response to additive noise excitations. We show that depending on noise…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
In the sensation of tones, visions and other stimuli, the "surround inhibition mechanism" (or "lateral inhibition mechanism") is crucial. The mechanism enhances the signals of the strongest tone, color and other stimuli, by reducing and…
We present the theory of a Josephson parametric amplifier employing two pump sources. Our calculations are based on Input-Output Theory, and can easily be generalized to any coupled system involving parametric interactions. We analyze the…
Powerful approaches to squeeze the motional state of a harmonic oscillator rely on the stepwise modulation of its resonance frequency. Such protocols can be limited by forces that vary slowly between experimental runs but are constant…
We undertake a detailed numerical study of the twin phenomena of stochastic and vibrational resonance in a discrete model system in the presence of bichromatic input signal. A two parameter cubic map is used as the model that combines the…
The problem of self-tuning a system to the Hopf bifurcation in the presence of noise and periodic external forcing is discussed. We find that the response of the system has a non-monotonic dependence on the noise-strength, and displays an…
A detailed analysis of the optical response of a system accommodating several coupled modes is needed for the complete understanding of the strong coupling effect. In this paper, we report on the analysis of scattering cross section spectra…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…