Related papers: Nonadiabatic escape and stochastic resonance
In this paper we analyze the global existence of classical solutions to the initial boundary-value problem for a nonlinear parabolic equation describing the collective behavior of an ensemble of neurons. These equations were obtained as a…
In this paper, we study the asymptotic behavior of a class of nonlinear Fokker-Planck type equations in a bounded domain with periodic boundary conditions. The system is motivated by our study of grain boundary dynamics, especially under…
Stochastic acceleration of charged particles due to interactions with magnetohydrodynamic (MHD) plasma waves is the dominant process leading to the formation of the high-energy electron and ion distributions in a variety of astrophysical…
We investigate the most probable phase portrait (MPPP) of a stochastic single-species model with the Allee effect using the non-local Fokker-Planck equation. This stochastic model is driven by non-Gaussian as well as Gaussian noise, and it…
We investigate variational methods for finding approximate solutions to the Fokker-Planck equation, especially in cases lacking detailed balance. These schemes fall into two classes: those in which a Hermitian operator is constructed from…
Many physical and chemical phenomena are governed by stochastic escape across potential barriers. The escape time depends on the structure of the noise and the shape of the potential barrier. By applying $\alpha$-stable noise from the…
We study the narrow escape problem in the disk, which consists in identifying the first exit time and first exit point distribution of a Brownian particle from the ball in dimension 2, with reflecting boundary conditions except on small…
This paper is devoted to Fokker-Planck and linear kinetic equations with very weak confinement corresponding to a potential with an at most logarithmic growth and no integrable stationary state. Our goal is to understand how to measure the…
Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Tran- sitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible…
We determine the incoherent spectrum, squeezing properties and second-order correlation function of the collective atomic degrees of freedom in absorptive optical bistability. This is accomplished via a linearized Fokker-Planck equation in…
We consider the problem of stochastic exit from a planar domain, whose boundary is an unstable periodic orbit, and which contains a stable periodic orbit. This problem arises when investigating the distribution of noise-induced phase slips…
The theory of stochastic resetting asserts that restarting a stochastic process can expedite its completion. In this paper, we study the escape process of a Brownian particle in an open Hamiltonian system that suffers noise-enhanced…
In this paper, we study the long-time behaviour of solutions to the Vlasov-Fokker-Planck equation where the confining potential is non-convex. This is a nonlocal nonlinear partial differential equation describing the time evolution of the…
We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as $V(x) \sim |x|^\alpha$, with $0 < \alpha < 1$. The probability density function $P(x,t)$ at long times…
We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
In neuroscience, the distribution of a decision time is modelled by means of a one-dimensional Fokker--Planck equation with time-dependent boundaries and space-time-dependent drift. Efficient approximation of the solution to this equation…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
The long-term mean-field dynamics of coupled underdamped Duffing oscillators driven by an external periodic signal with Gaussian noise is investigated. A Boltzmann-type H-theorem is proved for the associated nonlinear Fokker-Planck equation…
The main subject of the paper is an escape from a multi-well metastable potential on a time-scale of a formation of the quasi-equilibrium between the wells. The main attention is devoted to such ranges of friction in which an external…