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A noise-induced transition in the Lorenz system

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2004.12815v1.pdfWorking paper382.98 kBAdobe PDFView/Open
Title: A noise-induced transition in the Lorenz system
Authors: Zelati, MC
Hairer, M
Item Type: Working Paper
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.
Issue Date: 27-Apr-2020
URI: http://hdl.handle.net/10044/1/78729
Publisher: arXiv
Copyright Statement: © 2020 The Author(s)
Keywords: math.PR
math.PR
math.CA
math.DS
60H10, 37H20
math.PR
math.PR
math.CA
math.DS
60H10, 37H20
Publication Status: Published online
Appears in Collections:Pure Mathematics
Applied Mathematics and Mathematical Physics
Mathematics