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We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics.…
We study the real-time dynamics of a two-dimensional Anderson--Hubbard model using nonequilibrium self-consistent perturbation theory within the second-Born approximation. When compared with exact diagonalization performed on small…
In this paper we will study the asymptotic dynamics of fractional Navier-Stokes (NS) equations with additive white noise on three-dimensional torus $\mathbb T^3$. Under the conditions that the external forces $f(x)$ belong to the phase…
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…
This work is concerned about the asymptotic behavior of the solutions of the two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations driven by white noise with nonlinear diffusion terms. We prove the existence…
In this paper, we study the existence of SRB measures and their properties for infinite dimensional dynamical systems in a Hilbert space. We show several results including (i) if the system has a partially hyperbolic attractor with…
In this paper, we first introduce the definitions of random evolutionary system that associate with random evolutionary semigroup and the corresponding global weak or strong random attractor. Then we establish the existence result about…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
We present and study a novel class of one-dimensional Hilbert space eigenfunction transforms that diagonalize analytic difference operators encoding the (reduced) two-particle relativistic hyperbolic Calogero-Moser dynamics. The scattering…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
A parametric family of reaction-diffusion equations with nonlocal viscosity is considered. Existence of solutions and actually of pullback attractors is known from previous works. In this paper we obtain a robustness result of the…
In this paper, we mainly consider the long-time behavior of solutions for the Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions and two polynomial growth nonlinearities of arbitrary order. We prove the existence of a…
The long time behavior of Wong-Zakai approximations of 2D as well as 3D non-autonomous stochastic convective Brinkman-Forchheimer (CBF) equations with non-linear diffusion terms on bounded and unbounded ($\mathbb{R}^d$ for $d=2,3$) domains…
In this paper we first prove the existence and uniqueness of the solution to the stochastic Navier--Stokes equations on the rotating 2-dimensional sphere. Then we show the existence of an asymptotically compact random dynamical system…
We consider the stochastic evolution equation $ du=Audt+G(u)d\omega,\quad u(0)=u_0 $ in a separable Hilbert--space $V$. Here $G$ is supposed to be three times Fr\'echet--differentiable and $\omega$ is a trace class fractional…
Contraction theory for dynamical systems on Euclidean spaces is well-established. For contractive (resp. semi-contractive) systems, the distance (resp. semi-distance) between any two trajectories decreases exponentially fast. For partially…
In this article, we investigate the long-term dynamics of a class of two- and three-dimensional non-Newtonian fluids of differential type, known as third-grade fluids. We first show that when the external forcing is sufficiently small, the…
In this paper dynamic von Karman equations with localized interior damping supported in a boundary collar are considered. Hadamard well-posedness for von Karman plates with various types of nonlinear damping are well-known, and the…
We consider an autonomous system of partial differential equations for one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases…