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A noise-induced transition in the Lorenz system
File | Description | Size | Format | |
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2004.12815v1.pdf | Working paper | 382.98 kB | Adobe PDF | View/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 |