Related papers: The Stochastic Energy-Casimir Method
In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier--Stokes equations system on a torus with a degenerate, one dimensional noise. In particular, for some initial data and noises we…
We consider the orbital stability of relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We prove a persistence result for such relative…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
We establish unique existence and stability of subsonic potential flow for steady Euler-Poisson system in a multidimensional nozzle of a finite length when prescribing the electric potential difference on non-insulated boundary from a fixed…
The purpose of this work is to investigate the exponential stability of a second order coupled wave equations by laplacian with one locally internal viscous damping. Firstly, using a unique continuation theorem combined with a Carleman…
We consider a purely harmonic chain of oscillators which is perturbed by a stochastic noise. Under this perturbation, the system exhibits two conserved quantities: the volume and the energy. At the level of the hydrodynamic limit, under…
In this paper, we propose the diagonal implicit Runge-Kutta methods and transformed Runge-Kutta methods for stochastic Poisson systems with multiple noises. We prove that the first methods can preserve the Poisson structure, Casimir…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
For the Vlasov-Poisson equation with random uncertain initial data, we prove that the Landau damping solution given by the deterministic counterpart (Caglioti and Maffei, {\it J. Stat. Phys.}, 92:301-323, 1998) depends smoothly on the…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
The stability against perturbations of a dynamical system conserving a generalized phase-space volume is studied by exploiting the similarity between statistical physics formalism and that of ergodic theory. A general continuity theorem is…
In this work, we deal with the stochastic counterpart of the nonlocal Cahn-Hilliard equation with regular potential in a smooth bounded one-, two- or three-dimensional domain. The problem is endowed with homogeneous Neumann boundary…
We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arise. The stochastic resonance between the attractors of the…
We derive stochastic compressible Euler Equation from a Hamiltonian microscopic dynamics. We consider systems of interacting particles with H\"older noise and potential whose range is large in comparison with the typical distance between…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
We analyze the stochastic thermodynamics of systems with continuous space of states. The evolution equation, the rate of entropy production, and other results are obtained by a continuous time limit of a discrete time formulation. We point…
Results of stabilization for the higher order of the Kadomtsev-Petviashvili equation are presented in this manuscript. Precisely, we prove with two different approaches that under the presence of a damping mechanism and an internal delay…
Port-Hamiltonian systems are pertinent representations of many nonlinear physical systems. In this study, we formulate and analyse a general class of stochastic car-following models with a systematic port-Hamiltonian structure. The model…