相关论文: Global Dynamics of Granular Media Equations via St…

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…

In this work we extend the framework of monotone dynamical systems to a broad and important class of stochastic equations, namely cooperative McKean-Vlasov SDEs with multiplicative noise. Under a locally dissipative assumption, our main…

We develop a dynamical approach to infinite volume directed polymer measures in random environments. We define polymer dynamics in 1+1 dimension as a stochastic gradient flow on polymers pinned at the origin, for energy involving quadratic…

Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit…

This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: $(1)$ the equations contain locally Lipschitz nonlinear coupling…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…

In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…

Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective…

We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…

We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative…

We study invariant measures of continuous contact model in small dimensional spaces ($d =1,2$). Under general conditions we prove that in the critical regime this system has the one-parameter set of invariant measures parametrized by the…

In this work, we study non-asymptotic bounds on correlation between two time realizations of stable linear systems with isotropic Gaussian noise. Consequently, via sampling from a sub-trajectory and using \emph{Talagrands'} inequality, we…

We experimentally investigate the response of a sheared granular medium in a Couette geometry. The apparatus exhibits the expected stick-slip motion and we probe it in the very intermittent regime resulting from low driving. Statistical…

For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…

We consider the linear and quadratic higher order terms associated to the response of the statistical properties of a dynamical system to suitable small perturbations. These terms are related to the first and second derivative of the…

In this paper, we study concentration phenomena of zero-noise limits of invariant measures for stochastic differential equations defined on $\mathbb{R}^d$ with locally Lipschitz continuous coefficients and more than one ergodic state. Under…

In this article, we consider a novel version of three-dimensional (3D) globally modified Navier-Stokes (GMNS) system introduced by [Caraballo et. al., Adv. Nonlinear Stud. (2006), 6:411-436], which is very significant from the perspective…

Chaotic systems make long-horizon forecasts difficult because small perturbations in initial conditions cause trajectories to diverge at an exponential rate. In this setting, neural operators trained to minimize squared error losses, while…

We present a new microscopic model of granular medium to study the role of dynamical correlations and the onset of spatial order induced by the inelasticity of the interactions. In spite of its simplicity, it features several different…

In this paper, we consider the classical spin systems on unbounded lattices given by infinite-dimensional stochastic differential equations (SDEs). We assume that the stochastic forcing acts only on one particle. The other particles are not…