相关论文: Stochastic kinetics under combined action of two n…
The phenomenon of an excitable system producing a pulse under external or internal stimulation may be interpreted as a stochastic escape problem. This work addresses this issue by examining the Morris-Lecar neural model driven by symmetric…
We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by {\it white L\'evy noise} in a dynamical regime where inertial effects can safely be neglected. The…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
L\'evy noise influences diverse non-equilibrium systems across scales, including quantum devices, active biological matter, and financial markets. While such noise is pervasive, its overall impact on activated transitions between metastable…
Stochastic evolution of various dynamic systems and reaction networks is commonly described in terms of noise assisted escape of an overdamped particle from a potential well, as devised by the paradigmatic Langevin equation in which…
The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for…
Properties of the noise-driven escape kinetics are mainly determined by the stochastic component of the system dynamics. Nevertheless, the escape dynamics is also sensitive to deterministic forces. Here, we are exploring properties of the…
The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. Here, we explore properties of the escape of an inertial particle driven by L\'evy noise from a bounded domain,…
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…
We study the barrier crossing of a particle driven by white symmetric Levy noise of index $\alpha$ and intensity $DD for three different generic types of potentials: (a) a bistable potential; (b) a metastable potential; and (c) a truncated…
A dynamical system driven by non-Gaussian L\'evy noises of small intensity is considered. The first exit time of solution orbits from a bounded neighborhood of an attracting equilibrium state is estimated. For a class of non-Gaussian L\'evy…
The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently,…
For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent…
The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When…
It is a challenging issue to analyze complex dynamics from observed and simulated data. An advantage of extracting dynamic behaviors from data is that this approach enables the investigation of nonlinear phenomena whose mathematical models…
We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by compound Poisson shot noise and finite-measure L\'{e}vy noise. For each noise type, we compare trajectories of the…
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…
The mean first exit time and escape probability are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian alpha-stable type Levy motions. Both deterministic quantities are characterized by…
In this paper we provide an analysis of a mean first passage time problem of a random walker subject to a bi-variate $\alpha$-stable L\'evy type noise from a 2-dimensional disk. For an appropriate choice of parameters the mean first passage…
We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by L\'evy stable noises. The complexity of the first passage time statistics (mean first passage time,…