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arXiv · 2004.12815

A noise-induced transition in the Lorenz system

Michele Coti Zelati·Martin Hairer
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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.

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Michele Coti Zelati, Martin Hairer. 2020-04-27. A noise-induced transition in the Lorenz system. https://doi.org/10.1007/s00220-021-04000-6

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