Related papers: Stochastic perturbations to dynamical systems: a r…

A system's internal dynamics and its interaction with the environment can be determined by tracking how external perturbations affect its transition rates between states. Quantitative measurements of these rates are crucial for optimizing…

Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…

Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…

Stochastic forces in natural systems are rarely isotropic. From hydrodynamically coupled colloids to chemical reaction networks, noise contributions are inherently correlated. Together with internal interactions and changing environments,…

In this paper, we revisit energy-based concepts of controllability and reformulate them for control-affine nonlinear systems perturbed by white noise. Specifically, we discuss the relation between controllability of deterministic systems…

In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…

In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…

We illustrate a counter-intuitive effect of an additive stochastic force, which acts independently on each element of an ensemble of globally coupled oscillators. We show numerically and semi-analytically that a very small white noise is…

We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of Stochastic Resonance. We present a…

A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…

The influence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the equilibrium of the corresponding limiting system…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…

Biological systems (among others) may respond to a large variety of distinct external stimuli, or signals. These perturbations will generally be presented to the system not singly, but in various combinations, so that a proper understanding…

Many physical, chemical and biological systems exhibit a cooperative or sigmoidal response with respect to the input. In biochemistry, such behavior is called an allosteric effect. Here we demonstrate that a system with such properties can…

We consider the general response theory proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions…

In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…

Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…

Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving the statistical mean state of a turbulent system. In this work SSST is applied to the problem of understanding the…

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…