A noise-induced transition in the Lorenz system
Probability
2025-06-06 v4 Classical Analysis and ODEs
Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2004.12815,
title = {A noise-induced transition in the Lorenz system},
author = {Michele Coti Zelati and Martin Hairer},
journal= {arXiv preprint arXiv:2004.12815},
year = {2025}
}
Comments
Fixed a mathematical typo in Section 5