Precursors to rare events in stochastic resonance

Author:

Giorgini L. T.,Lim S. H.,Moon W.,Wettlaufer J. S.

Abstract

Abstract In stochastic resonance, a periodically forced Brownian particle in a double-well potential jumps between minima at rare increments, the prediction of which poses a major theoretical challenge. Here, we use a path-integral method to find a precursor to these transitions by determining the most probable (or “optimal”) space-time path of a particle. We characterize the optimal path using a direct comparison principle between the Langevin and Hamiltonian dynamical descriptions, allowing us to express the jump condition in terms of the accumulation of noise around the stable periodic path. In consequence, as a system approaches a rare event these fluctuations approach one of the deterministic minimizers, thereby providing a precursor for predicting a stochastic transition. We demonstrate the method numerically, which allows us to determine whether a state is following a stable periodic path or will experience an incipient jump with a high probability. The vast range of systems that exhibit stochastic resonance behavior insures broad relevance of our framework, which allows one to extract precursor fluctuations from data.

Publisher

IOP Publishing

Subject

General Physics and Astronomy

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Thermodynamic cost of erasing information in finite time;Physical Review Research;2023-05-09

2. Predicting critical transitions in multiscale dynamical systems using reservoir computing;Chaos: An Interdisciplinary Journal of Nonlinear Science;2020-12

3. Extending Transition Path Theory: Periodically Driven and Finite-Time Dynamics;Journal of Nonlinear Science;2020-09-10

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