相关论文: Stationary states in 2D systems driven by bi-varia…
Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises,…
A L\'evy noise is an efficient description of out-of-equilibrium systems. The presence of L\'evy flights results in a plenitude of noise-induced phenomena. Among others, L\'evy flights can produce stationary states with more than one modal…
Stationary states for a particle moving in a single-well, steeper than parabolic, potential driven by L\'evy noise can be bi-modal. Here, we explore in details conditions that are required in order to induce multimodal stationary states…
Using methods of stochastic dynamics, we have studied stationary states in the underdamped anharmonic stochastic oscillators driven by Cauchy noise. Shape of stationary states depend both on the potential type and the damping. If the…
We discuss the existence of stationary states for subharmonic potentials $V(x) \propto |x|^c$, $c<2$, under action of symmetric $\alpha$-stable noises. We show analytically that the necessary condition for the existence of the steady state…
Properties of stochastic systems are defined by the noise type and deterministic forces acting on the system. In out-of-equilibrium setups, e.g., for motions under action of L\'evy noises, the existence of the stationary state is not only…
Complex dynamical systems which are governed by anomalous diffusion often can be described by Langevin equations driven by L\'evy stable noise. In this article we generalize nonlinear stochastic differential equations driven by Gaussian…
Noise induced jumping between meta-stable states in a potential depends on the structure of the noise. For an $\alpha$-stable noise, jumping triggered by single extreme events contributes to the transition probability. This is also called…
We study the properties of the probability density function (PDF) of a bistable system driven by heavy tailed white symmetric L\'evy noise. The shape of the stationary PDF is found analytically for the particular case of the L\'evy index…
We demonstrate occurrence of bimodality and dynamical hysteresis in a system describing an overdamped quartic oscillator perturbed by additive white and asymmetric L\'evy noise. Investigated estimators of the stationary probability density…
A stationary wave pattern occurring in a flow of a two-component Bose-Einstein condensate past an obstacle is studied. We consider the general case of unequal velocities of two superfluid components. The Landau criterium applied to the…
The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillations regime and the excitable one are described. The first regime consists in the coexistence of two stable limit cycles in the phase…
We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients,…
Planar travelling waves on $\mathbb R^d,$ with $ d\geq 2,$ are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescales with high probability, provided that the wave is orbitally…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
Azimuthal instabilities occur in rotationally symmetric systems, either as spinning (rotating) waves or standing waves. We make use of a novel ansatz to derive a differential equation characterizing the state of these instabilities in terms…
Stationary states of overdamped anharmonic stochastic oscillators driven by L\'evy noise are typically multimodal. The very same situation is recorded for an underdamped L\'evy noise driven motion in single-well potentials with linear…
Stabilization of non-stationary linear systems over noisy communication channels is considered. Stochastically stable sources, and unstable but noise-free or bounded-noise systems have been extensively studied in information theory and…
We study the overdamped motion of a Brownian particle in a driven double-well system to understand various physical phenomena observed experimentally. These phenomena include hysteresis, stochastic resonance, and net unidirectional motion…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…