相关论文: Phase Reduction in the Noise Induced Escape Proble…

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…

We consider slow-fast systems of differential equations, in which both the slow and fast variables are perturbed by noise. When the deterministic system admits a uniformly asymptotically stable slow manifold, we show that the sample paths…

The well-posedness of a phase-field approximation to the Willmore flow with volume constraint is established. The existence proof relies on the underlying gradient flow structure of the problem: the time discrete approximation is solved by…

We study the large deviations of a simple noise-perturbed dynamical system having continuous sets of steady states, which mimick those found in some partial differential equations related, for example, to turbulence problems. The system is…

This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…

We employ a typical genetic circuit model to explore how noise can influence the dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure…

We perform a convergence analysis of a discrete-in-time minimization scheme approximating a finite dimensional singularly perturbed gradient flow. We allow for different scalings between the viscosity parameter $\varepsilon$ and the time…

We study the effect of noise-enhanced stability of periodically driven metastable states in a system described by piecewise linear potential. We find that the growing of the average escape time with the intensity of the noise is depending…

A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…

The motion of weakly inertial Brownian particles, transported by steady two-dimensional fluid flows, is investigated by means of asymptotic methods. We focus on the phenomenon of noise-induced separatrix crossing, which can force particles…

The analysis of noise-induced escape in populations of bistable elements is challenging, because nonlinearity, coupling, and noise all play essential roles. We show that the interplay of these three factors yields three qualitatively…

Recent progress in robust statistical learning has mainly tackled convex problems, like mean estimation or linear regression, with non-convex challenges receiving less attention. Phase retrieval exemplifies such a non-convex problem,…

An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…

Driven-dissipative quantum systems can recover stable dynamical attractors in the semiclassical limit, including coexisting limit cycles. At finite fluctuation strength, this classical coexistence becomes quantum metastability: the…

We consider a finite dimensional deterministic dynamical system with a global attractor A with a unique ergodic measure P concentrated on it, which is uniformly parametrized by the mean of the trajectories in a bounded set D containing A.…

The stability of shear flows of electrically conducting fluids, with respect to finite amplitude three-dimensional localized disturbances is considered. The time evolution of the fluid impulse integral, characterizing such disturbances, for…

In this paper we present a general result with an easily checkable condition that ensures a transition from chaotic regime to regular regime in random dynamical systems with additive noise. We show how this result applies to a prototypical…

We consider in this work small random perturbations (of multiplicative noise type) of the gradient flow. We prove that under mild conditions, when the potential function is a Morse function with additional strong saddle condition, the…

In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse…

In this paper, we discuss selected adjoint approaches for the turbulent flow control. In particular, we focus on the application of adjoint solvers for the scope of noise reduction, in which flow solutions are obtained by large eddy and…