Related papers: Epigenetics as a first exit problem

It has recently been shown that traversable wormholes may be supported by phantom energy. In this work phantom wormhole geometries are modelled by matching an interior traversable wormhole solution, governed by the equation of state…

In this paper, we consider stochastic two-phase Stefan problem driven by general jump L\'evy noise. We first obtain the existence and uniqueness of the strong solution and then establish the ergodicity of the stochastic Stefan problem.…

We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…

In this paper we are concerned with the stability of equilibrium solutions of periodic Hamiltonian systems with one degree of freedom in the case of degeneracy, which means that the characteristic exponents of the linearized system have…

A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node…

A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…

The unpredictability in chaotic scattering problems is a fundamental topic in physics that has been studied either in purely conservative systems or in the presence of weak perturbations. In many systems noise plays an important role in the…

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…

Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…

Positive definiteness of a Hamiltonian expanded about an equilibrium point provides only a necessary condition for stability, a criterion known as Dirichlet's theorem. The reason that this criterion is not necessary for stability is because…

We present a study of the noise driven escape of an overdamped Brownian particle moving in a cubic potential profile with a metastable state. We analyze the role of the initial conditions of the particle on the enhancement of the average…

We consider noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable…

In multicellular organisms, cells differentiate into several distinct types during early development. Determination of each cellular state, along with the ratio of each cell type, as well as the developmental course during cell…

The steady state in three-level lambda and ladder systems is studied. It is well-known that in a lambda system this steady state is the coherent population trapping state, independent of the presence of spontaneous emission. In contrast,…

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence…

There is an abundance of evidence that some relaxation dynamics, e.g., exponential decays, are much more common in nature than others. Recently, there have been attempts to trace this dominance back to a certain stability of the prevalent…

We obtain the first probabilistic proof of continuous differentiability of time-dependent optimal boundaries in optimal stopping problems. The underlying stochastic dynamics is a one-dimensional, time-inhomogeneous diffusion. The gain…

This article studies a linear scalar delay differential equation subject to small multiplicative power tail L\'evy noise. We solve the first passage (the Kramers) problem with probabilistic methods and discover an asymptotic loss of memory…

We construct a stochastic dynamical systems theory in which sustainability is a structural boundary property of a fully coupled Earth--Human--Production system. Each subsystem is modelled as a vector-valued process governed by stochastic…

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…