Related papers: Long exit times near a repelling equilibrium
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,…
This paper is concerned with the problem of Model Predictive Control and Rolling Horizon Control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a…
We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a…
We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than the computation of the probability density. The main…
A theoretical approach for characterising the influence of asymmetry of noise distribution on the escape rate of a multi-stable system is presented. This was carried out via the estimation of an action, which is defined as an exponential…
In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the…
Consider a two-dimensional continuous-time dynamical system, with an attracting fixed point $S$. If the deterministic dynamics are perturbed by white noise (random perturbations) of strength $\epsilon$, the system state will eventually…
The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise-intensity (weak, intermediate, and strong-noise) are identified by performing a…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
We report on the effect of noise on the characteristics of the bistable polariton emission system. The present experiment provides a time resolved access to the polariton emission intensity. We evidence the noise-induced transitions between…
We derive asymptotics for the quenched probability that a critical branching Brownian motion killed at a small rate in Poissonian obstacles exits a large domain. Results are formulated in terms of the solution to a semilinear partial…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. It is known that, for discrete-time systems, the power-law exponent decreases as the…
We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…
We study the zeros and critical points of different indices of the standard Gaussian entire function on the complex plane (whose zero set is stationary). We provide asymptotics for the second order correlations of all the corresponding…
We study asymptotic properties of the Generalized Langevin Equation (GLE) in the presence of a wide class of external potential wells with a power-law decay memory kernel. When the memory can be expressed as a sum of exponentials, a class…
This paper considers the motion of an object subjected to dry friction and an external random force. The objective is to characterize the role of the correlation time of the external random force. We develop efficient stochastic simulation…
The Lasserre or moment-sum-of-square hierarchy of linear matrix inequality relaxations is used to compute inner approximations of the maximal positively invariant set for continuous-time dynamical systems with polynomial vector fields.…
We explore the effects of spatial locality on the dynamics of random quantum systems subject to a Markovian noise. To this end, we study a model in which the system Hamiltonian and its couplings to the noise are random matrices whose…