Noise-Induced Escape From the Lorenz Attractor

Abstract

Noise-induced escape from a quasi-hyperbolic attractor in the Lorenz system is investigated via an analysis of the distributions of both the escape trajectories and the corresponding realizations of the random force. It is shown that a unique escape path exists, and that it consists of three parts with noise playing a different role in each. It is found that the mechanism of the escape from a quasi-hyperbolic attractor differs from that of escape from a non-hyperbolic attractor. The possibility of calculating the escape probability is discussed.

Noise-induced escape in an excitable system

“…Such a picture has a rigorous basis in the theory of large fluctuations [18] and it has been confirmed in many examples ranging from a simple overdamped bistable system [22] to systems with chaotic dynamics [23][24][25][26]. The saddle state is considered as the transition state and is used for calculation of the escape rate.…”

Stochastic approach for assessing the predictability of chaotic time series using reservoir computing

“…This deviation happens in the region of splitting stable manifold of the saddle point of system (1) 17 . It has been shown 32,33 that this region is responsible for large deviations from the chaotic attractor. Fig.…”

Stochastic approach for assessing the predictability of chaotic time series using reservoir computing

“…This deviation happens in the region of splitting stable manifold of the saddle point of system (1) 17 . It has been shown 32,33 that this region is responsible for large deviations from the chaotic attractor. Fig.…”