Related papers: Escape Rates in Bistable Systems Induced by Quasi-…
The dynamics of mechanical systems such as turbomachinery with multiple blades are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and…
The effect of noise is studied in one-dimensional maps undergoing transcritical, tangent, and pitchfork bifurcations. The attractors of the noiseless map become metastable states in the presence of noise. In the weak-noise limit, a…
Escape from a potential well is an extreme example of transient behavior. We consider the escape of the harmonically forced particle under viscous damping from the benchmark truncated weakly nonlinear potential well. Main attention is paid…
The problem of noise-induced transitions is often associated with Hendrik Kramers due to his seminal paper of 1940, where an archetypal example - one-dimensional potential system subject to linear damping and weak white noise - was…
We study the noise-induced escape from a stable limit cycle of a non-gradient dynamical system driven by a small additive noise. The fact that the optimal transition path in this case is infinitely long imposes a severe numerical challenge…
We treat the noise-activated escape from a one-dimensional potential well of an overdamped particle, to which a periodic force of fixed frequency is applied. We determine the boundary layer behavior, and the physically relevant length…
In various models and systems involving the escape of periodically forced particle from the potential well, a common pattern is observed. Namely, the minimal forcing amplitude required for the escape exhibits sharp minimum for the…
It is well known that the addition of noise in a multistable system can induce random transitions between stable states. The rate of transition can be characterised in terms of the noise-free system's dynamics and the added noise: for…
We study the noise-driven escape of active Brownian particles (ABPs) and run-and-tumble particles (RTPs) from confining potentials. In the small noise limit, we provide an exact expression for the escape rate in term of a variational…
We consider a simple model of a bistable system under the influence of multiplicative noise. We provide a path integral representation of the overdamped Langevin dynamics and compute conditional probabilities and escape rates in the weak…
Stochastic motion in a bistable, periodically modulated potential is discussed. The system is stimulated by a white noise increments of which have a symmetric stable L\'evy distribution. The noise is multiplicative: its intensity depends on…
This paper focuses on the escape problem of a harmonically-forced classical particle from a purely-quartic truncated potential well. The latter corresponds to various engineering systems that involve purely cubic restoring force and absence…
When tunneling occurs out of generic initial states, a significant fraction of probability is lost at early times during which the dynamics is governed by excited resonance states. However, first-principles analyses based on path integrals…
We investigate the escape rate of an overdamped, self-propelled spherical Brownian particle on a surface from a metastable potential well. Within a modeling in terms of a 1D constant speed of the particle's active dynamics we consider the…
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of…
Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these…
We examine the mean first passage time for a particle driven by highly correlated Gaussian fluctuations to reach one or more predetermined boundaries. We discuss a numerical algorithm to generate power-law correlated fluctuations and apply…
Many phenomena in nature are described by excitable systems driven by colored noise. The temporal correlations in the fluctuations hinder an analytical treatment. We here present a general method of reduction to a white-noise system,…
In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in…
We provide a complete solution of the problems of the probability distribution and the escape rate in Poisson-noise driven systems. It includes both the exponents and the prefactors. The analysis refers to an overdamped particle in a…