Related papers: Escape from attracting sets in randomly perturbed …
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,…
It is a common phenomenon in nature and technology that a system under perturbations exits a regime of its usual dynamics. Often it is possible to define a potential function whereby a potential well can be associated with a usual or…
The analysis of noise-induced escape in populations of bistable elements is challenging, because nonlinearity, coupling, and noise all play essential roles. We show that the interplay of these three factors yields three qualitatively…
The rate of noise-induced escape from a metastable state of a periodically modulated overdamped system is found for an arbitrary modulation amplitude $A$. The instantaneous escape rate displays peaks that vary with the modulation from…
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
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…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
A natural question of how the survival probability depends upon a position of a hole was seemingly never addressed in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related…
A new approach for the weak noise analysis of exit problems removes an intrinsic contradiction of an existing method. It applies for both the mean time and the location of the exits; novel outcomes mainly concern the exits from entire…
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…
We present a general geometrical approach to the problem of escape from a metastable state in the presence of noise. The accompanying analysis leads to a simple condition, based on the norm of the drift field, for determining whether…
We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…
A control strategy is employed that modifies the stochastic escape times from one basin of attraction to another in a model of a double-gyre flow. The system studied captures the behavior of a large class of fluid flows that circulate and…
The aim of this work is to revise but also explore even further the escape dynamics in the H\'{e}non-Heiles system. In particular, we conduct a thorough and systematic numerical investigation distinguishing between trapped (ordered and…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
We reveal the escape mechanism of orbits in a Hamiltonian system with four exit channels composed of two-dimensional perturbed harmonic oscillators. We distinguish between trapped chaotic, non-escaping regular and escaping orbits by…
Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For…
The noise-enhanced trapping is a surprising phenomenon that has already been studied in chaotic scattering problems where the noise affects the physical variables but not the parameters of the system. Following this research, in this work…
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…
Many-body and complex systems, both classical and quantum, often exhibit slow, nonlinear relaxation toward stationary states due to the presence of metastable configurations and environmental fluctuations. Nonlinear relaxation in a wide…