Related papers: Most probable transition paths in piecewise-smooth…
We consider noise-induced transition paths in randomly perturbed dynami- cal systems on a smooth manifold. The classical Freidlin-Wentzell large devia- tion theory in Euclidean spaces is generalized and new forms of action functionals are…
Stochastic systems are used to model a variety of phenomena in which noise plays an essential role. In these models, one potential goal is to determine if noise can induce transitions between states, and if so, to calculate the most…
Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian L\'evy noise. Among these complex phenomena, the most…
The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems. The computation of the most probable paths is a key issue to understand the mechanism of…
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We…
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…
This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric $\alpha$-stable L\'{e}vy motion ($0<\alpha<1$) or Brownian motion. For stochastic dynamical systems…
Sliding motion is evolution on a switching manifold of a discontinuous, piecewise-smooth system of ordinary differential equations. In this paper we quantitatively study the effects of small-amplitude, additive, white Gaussian noise on…
The probability of trajectories of weakly diffusive processes to remain in the tubular neighbourhood of a smooth path is given by the Freidlin-Wentzell-Graham theory of large deviations. The most probable path between two states (the…
In multistable dynamical systems driven by weak Gaussian noise, transitions between competing states are often assumed to pass via a saddle on the separating basin boundary. By contrast, we show that timescale separation can cause saddle…
Path integrals play a crucial role in describing the dynamics of physical systems subject to classical or quantum noise. In fact, when correctly normalized, they express the probability of transition between two states of the system. In…
Turbulence transition often arises from a subcritical transition between bistable states characterized by invariant sets of deterministic dynamical systems, and such transitions can be triggered by system noise as rare events. In this…
This paper presents a heuristic derivation of a geometric minimum action method that can be used to determine most-probable transition paths in noise-driven dynamical systems. Particular attention is focused on systems that violate detailed…
Many natural systems exhibit phase transition where external environmental conditions spark a shift to a new and sometimes quite different state. Therefore, detecting the behavior of a stochastic dynamic system such as the most probable…
Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often…
The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager-Machlup action functional and can be described by a necessary but not sufficient condition, the Euler-Lagrange equation (a…
Rate-induced tipping occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states. We show that the addition of noise to the system can cause it to tip well below the critical rate at…
We demonstrate the possibility to systematically steer the most probable escape paths (MPEPs) by adjusting relative noise intensities in dynamical systems that exhibit noise-induced escape from a metastable point via a saddle point. Using a…
In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data and has become an advantageous tool for us to study complex…
Stochastic vegetation-water dynamical systems play a pivotal role in ecological stability, biodiversity, water resource management, and adaptation to climate change. This research proposes a machine learning-based method for analyzing rare…