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A noise-induced transition in the Lorenz system

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arxiv 2004.12815 v4 pith:AJOYC574 submitted 2020-04-27 math.PR math.CAmath.DS

Michele Coti Zelati , Martin Hairer This is my paper · ORCID
classification math.PRmath.CAmath.DS
keywords noiseinvariantcausesergodiclorenzmeasuresystemtransition
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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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Cited by 2 Pith papers

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