Related papers: Output-only parameter identification of a colored-…
The aim of this short note is to show that Denoising Diffusion Probabilistic Model DDPM, a non-homogeneous discrete-time Markov process, can be represented by a time-homogeneous continuous-time Markov process observed at non-uniformly…
In the thermodynamic limit, the time evolution of isolated long-range interacting systems is properly described by the Vlasov equation. This equation admits non-equilibrium dynamically stable stationary solutions characterized by a zero…
Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel…
The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is…
We discover presence of a hitherto unexplored type of resonance in a parametrically excited Van der Pol oscillator. The oscillator also possesses a state of anti-resonance. In the weak non-linear limit, we explain how to practically get a…
A van der Pol self sustained oscillator with higher order nonlinearity exhibits a rich dynamics, with multiple periodic attractors, and still the model allows analytical approximations. Some of these properties can be conveniently exploited…
We present the numerical estimation of noise parameter induced in the dynamics of the variables by random particle interactions involved in the stochastic chemical oscillator and use it as order parameter to detect the transition from…
In this study, we consider the experimentally-obtained, periodically-forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions…
Cross-spectrum analysis is a commonly-used technique for the detection of phase and amplitude noise of a signal in the presence of interfering noise. It extracts the desired correlated noise from two time series in the presence of…
This paper considers the oscillations modeled by a forced Van der Pol generalized oscillator. These oscillations are described by a nonlinear differential equation of the form $…
We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a…
In this article, we study the problem of parameter estimation for a discrete Ornstein - Uhlenbeck model driven by Poisson fractional noise. Based on random walk approximation for the noise, we study least squares and maximum likelihood…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…
We consider equations of nonlinear transport on the circle with regular self interactions appearing in aggregation models and deterministic mean field dynamics. We introduce a random perturbation of such systems through a stochastic…
Nonlinear oscillators are a key modelling tool in many applications. The influence of annealed noise on nonlinear oscillators has been studied intensively. It can induce effects in nonlinear oscillators not present in the deterministic…
We consider the identification of nonlinear heat conduction laws in stationary and instationary heat transfer problems. Only a single additional measurement of the temperature on a curve on the boundary is required to determine the unknown…
In reacting flow systems, thermoacoustic instability characterized by high amplitude pressure fluctuations, is driven by a positive coupling between the unsteady heat release rate and the acoustic field of the combustor. When the underlying…
Many physical and biological systems exhibit intrinsic cyclic dynamics that are altered by random external perturbations. We examine continuous-time autonomous dynamical systems exhibiting a stable limit cycle, perturbed by additive…
We present a study of the escape time from a metastable state of an overdamped Brownian particle, in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of…
The paper addresses the critical problem of identifying unknown parameters of an atomic clock ensemble. The ensemble model is considered as a set of individual clock models, where each clock is described by a second-order linear stochastic…