A noise-induced transition in the Lorenz system

Fuente: arXiv
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Main Authors: Zelati, Michele Coti, Hairer, Martin
Format: Preprint
Published: 2020
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author Zelati, Michele Coti
Hairer, Martin
author_facet Zelati, Michele Coti
Hairer, Martin
contents We consider a stochastic perturbation of the classical Lorenz system in the range of parameters for which the origin is the global attractor. We show that adding noise in the last component causes a transition from a unique to exactly two ergodic invariant measures. The bifurcation threshold depends on the strength of the noise: if the noise is weak, the only invariant measure is Gaussian, while strong enough noise causes the appearance of a second ergodic invariant measure.
format Preprint
id arxiv_https___arxiv_org_abs_2004_12815
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle A noise-induced transition in the Lorenz system
Zelati, Michele Coti
Hairer, Martin
Probability
Classical Analysis and ODEs
Dynamical Systems
60H10, 37H20
We consider a stochastic perturbation of the classical Lorenz system in the range of parameters for which the origin is the global attractor. We show that adding noise in the last component causes a transition from a unique to exactly two ergodic invariant measures. The bifurcation threshold depends on the strength of the noise: if the noise is weak, the only invariant measure is Gaussian, while strong enough noise causes the appearance of a second ergodic invariant measure.
title A noise-induced transition in the Lorenz system
topic Probability
Classical Analysis and ODEs
Dynamical Systems
60H10, 37H20
url https://arxiv.org/abs/2004.12815