Related papers: Reconstructing resonant phase oscillator interacti…

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…

Model-free reconstruction of the bifurcation diagrams of Chua's circuits by the technique of parameter-aware reservoir computing is investigated. We demonstrate that: (1) reservoir computer can be utilized as a noise filter to recover the…

Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display…

We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic…

We consider classical nonlinear oscillators on hexagonal lattices. When the coupling between the elements is repulsive, we observe coexisting states, each one with its own basin of attraction. These states differ by their degree of…

The paper documents the development of a novel time-domain model of injection-locked oscillator phase-noise response. The methodology follows a first-principle approach and applies to all circuit topologies, coupling configurations,…

We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…

One unique feature of nonlinear dynamical systems is the existence of superharmonic and subharmonic resonances in addition to primary resonances. In this study, an effective vibration testing methodology is introduced for the experimental…

The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive…

Fluctuations in a vast range of physical systems can be described as a superposition of uncorrelated pulses with a fixed shape, a process commonly referred to as a (generalized) shot noise or a filtered Poisson process. In this…

A common problem in the sciences is that a signal of interest is observed only indirectly, through smooth functionals of the signal whose values are then obscured by noise. In such inverse problems, the functionals dampen or entirely…

Inverse stochastic resonance comprises a nonlinear response of an oscillatory system to noise where the frequency of noise-perturbed oscillations becomes minimal at an intermediate noise level. We demonstrate two generic scenarios for…

As circuits continue to miniaturize, noise has become a significant obstacle to performance optimization. Stochastic resonance in logic circuits offers an innovative approach to harness noise constructively; however, current implementations…

We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of the scattered waves associated with incident plane waves sent from one direction but at multiple frequencies. We define, for each frequency,…

We prove that low-rank matrices can be recovered efficiently from a small number of measurements that are sampled from orbits of a certain matrix group. As a special case, our theory makes statements about the phase retrieval problem. Here,…

In recent years, there is a growing need for processing methods aimed at extracting useful information from large datasets. In many cases the challenge is to discover a low-dimensional structure in the data, often concealed by the existence…

This work presents the development of an online parameter estimation algorithm for the identification of resonating modes in a linear system of arbitrary order. The method employs a short-time Fourier transform of the input and output…

We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…

Analyzing data from paleoclimate archives such as tree rings or lake sediments offers the opportunity of inferring information on past climate variability. Often, such data sets are univariate and a proper reconstruction of the system's…

Non-autonomous perturbations of isochronous systems in the plane are considered. It is assumed that the intensity of perturbations decays with time, and the frequency is asymptotically constant with the limiting value satisfying a resonance…