Related papers: The Escape Problem for Irreversible Systems
The time-dependent barrier passage of an anomalous system-reservoir coupling non-equilibrium open environment is studied where the heat bath is modulated by an external noise. The time-dependent barrier passing probability is obtained…
We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which…
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with…
Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient…
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…
The paper considers a process of escape of classical particle from a one-dimensional potential well by virtue of an external harmonic forcing. We address a particular model of the infinite-range potential well that allows independent…
Neuronal networks can generate burst events. It remains unclear how to analyse interburst periods and their statistics. We study here the phase-space of a mean-field model, based on synaptic short-term changes, that exhibit burst and…
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…
The escape probability is a deterministic concept that quantifies some aspects of stochastic dynamics. This issue has been investigated previously for dynamical systems driven by Gaussian Brownian motions. The present work considers escape…
For overdamped Langevin systems subjected to weak thermal noise and nonconservative forces, we establish a connection between Freidlin-Wentzell large deviations theory and stochastic thermodynamics. First, we derive a series expansion of…
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…
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.…
Metastability in open system dynamics describes the phenomena of initial relaxation to longlived metastable states before decaying to the asymptotic stable states. It has been predicted in continuous-time stochastic dynamics of both…
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…
In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…
We consider certain one dimensional ordinary stochastic differential equations driven by additive Brownian motion of variance $\varepsilon ^2$. When $\varepsilon =0$ such equations have an unstable non-hyperbolic fixed point and the drift…
The narrow escape problem is a first-passage problem concerned with randomly moving particles in a physical domain, being trapped by absorbing surface traps (windows), such that the measure of traps is small compared to the domain size. The…
We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed…
Effects of non-Gaussian $\alpha-$stable L\'evy noise on the Gompertz tumor growth model are quantified by considering the mean exit time and escape probability of the cancer cell density from inside a safe or benign domain. The mean exit…
We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…