Related papers: Phase-Amplitude Description of Stochastic Oscillat…

In this study, we introduce a sensitivity analysis methodology for stochastic systems in chemistry, where dynamics are often governed by random processes. Our approach is based on gradient estimation via finite differences, averaging…

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…

This paper proposes an efficient method for the calculation of the stabilization parameters in RF power amplifiers operating in periodic large-signal regimes. Stabilization is achieved by applying the principles of linear control theory for…

The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that…

Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results have been obtained for weakly perturbed oscillators that…

We analyze the effect of additive fractional noise with Hurst parameter $H > \frac{1}{2}$ on fast-slow systems. Our strategy is based on sample paths estimates, similar to the approach by Berglund and Gentz in the Brownian motion case. Yet,…

We propose a stochastic MPC scheme using an optimization over the initial state for the predicted trajectory. Considering linear discrete-time systems under unbounded additive stochastic disturbances subject to chance constraints, we use…

We introduce a stochastic model for the determination of phase noise in optoelectronic oscillators. After a short overview of the main results for the phase diffusion approach in autonomous oscillators, an extension is proposed for the case…

We study single-variable approaches for describing stochastic dynamics with small inertia. The basic models we deal with describe passive Brownian particles and phase elements (phase oscillators, rotators, superconducting Josephson…

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multi-dimensional space the phases (in the sense of phase…

We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a…

We analyze an intermediate collective regime where amplitude oscillators distribute themselves along a closed, smooth, time-dependent curve $\mathcal{C}$, thereby maintaining the typical ordering of (identical) phase oscillators. This is…

We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…

We present stochastic variants of the exponential time differencing schemes for stiff stochastic differential equations. We derive three explicit schemes that offer better stability compared to Euler-Maruyama and Milstein's method, and…

We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only…

The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…

Stochastic parametrisations are used in weather and climate models to improve the representation of unpredictable unresolved processes. When compared to a deterministic model, a stochastic model represents `model uncertainty', i.e., sources…

A recently proposed method for computer simulations in the isothermal-isobaric (NPT) ensemble, based on Langevin-type equations of motion for the particle coordinates and the ``piston'' degree of freedom, is re-derived by straightforward…

Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…

We prove a sharp asymptotic formula for certain oscillatory integrals that may be approached using the stationary phase method. The estimates are uniform in terms of auxiliary parameters, which is crucial for application in analytic number…