Related papers: State selection in the noisy stabilized Kuramoto-S…
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…
We focus in this paper on the stochastic stabilization problems of PDEs by Levy noise. Sufficient conditions under which the perturbed systems decay exponentially with a general rate function are provided and some examples are constructed…
We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…
In this paper, two boundary controllers are proposed to stabilize the origin of the nonlinear Kuramoto-Sivashinsky equation under intermittent measurements. More precisely, the spatial domain is divided into two sub-domains. The state of…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
The unavoidable interaction of quantum systems with their environment usually results in the loss of desired quantum resources. Suitably chosen system Hamiltonians, however, can, to some extent, counteract such detrimental decay, giving…
This paper provides a stabilizing preparation method for quantum Gaussian states by utilizing continuous measurement. The stochastic evolution of the open quantum system is described in terms of the quantum stochastic master equation. We…
The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. This…
In this paper, the successive approximation method is applied to investigate the existence and uniqueness of solutions to the stochastic differential equations (SDEs) driven by L\'evy noise under non-Lipschitz condition which is a much…
We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…
The stabilisation by noise on the boundary of the Chafee-Infante equation with dynamical boundary conditions subject to a multiplicative It\^o noise is studied. In particular, we show that there exists a finite range of noise intensities…
We revisit the convergence analysis of constant stepsize stochastic approximation (SA) with decision-dependent Markovian noise, with a focus on characterizing the stationary bias against the root of the mean-field equation. We first…
We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is…
We study open quantum systems whose evolution is governed by a master equation of Kossakowski-Gorini-Sudarshan-Lindblad type and give a characterization of the convex set of steady states of such systems based on the generalized Bloch…
We consider the problem of state selection for a stochastic system, initially in an unstable stationary state, when multiple metastable states compete for occupation. Using path-integral techniques we derive remarkably simple and accurate…
Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…
The effect of particles that undergo strong diffusive-shock-acceleration on the stability of the accelerating shock is investigated. A two-fluid model is employed in which the accelerated particles are treated as a fluid whose effect is…
In this paper, we study the backward problem of determining initial condition for some class of nonlinear parabolic equations in multidimensional domain where data are given under random noise. This problem is ill-posed, i.e., the solution…
By the example of a kicked quartic oscillator we investigate the dynamics of classically chaotic quantum systems with few degrees of freedom affected by persistent external noise. Stability and reversibility of the motion are analyzed in…
We present the global-in-time existence of strong solutions and its large-time behavior for the Kuramoto-Sakaguchi equation with inertia. The equation describes the evolution of the probability density function for a large ensemble of…