Related papers: Exact results for a noise-induced bistable system
We proposed the modified version of quantum-mechanical theory of continuous measurements for the case of classical open systems. In our approach the influence of measurement on evolution of distribution function of an open system is…
We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete 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…
We present approximate analytical method of analysis of stationary states of nonlinear quantum systems with the noise. As an example we consider quantum nonlinear oscillator excited by fluctuating force and found parameter regions with more…
In this paper, we extend the energy-Casimir stability method for deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions for the stability in probability of stochastic dynamical systems with symmetries and…
Genetic switch systems with mutual repression of two transcription factors are studied using deterministic methods (rate equations) and stochastic methods (the master equation and Monte Carlo simulations). These systems exhibit bistability,…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
In this paper, the problem of non-fragile finite-time stabilization for linear discrete mean-field stochastic systems is studied. The uncertain characteristics in control parameters are assumed to be random satisfying the Bernoulli…
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced…
The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and…
It is well known that the addition of noise in a multistable system can induce random transitions between stable states. The rate of transition can be characterised in terms of the noise-free system's dynamics and the added noise: for…
This paper numerically investigates the mean first passage time (MFPT) and phase transition of a bistable Duffing system driven by L\'evy stable noise, which can reduce to the common Gaussian noise with the stability index 2. We obtain the…
Sliding motion is evolution on a switching manifold of a discontinuous, piecewise-smooth system of ordinary differential equations. In this paper we quantitatively study the effects of small-amplitude, additive, white Gaussian noise on…
We study the convergence of a Zakharov system driven by a time white noise, colored in space, to a multiplicative stochastic nonlinear Schr{\"o}dinger equation, as the ion-sound speed tends to infinity. In the absence of noise, the…
The statistics of transitions between the metastable states of a periodically driven bistable Brownian oscillator are investigated on the basis of a two-state description by means of a master equation with time-dependent rates. The results…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose we consider the motion of a particle subjected to dry friction and coloured noise. The finite correlation time…
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…