A Noise-Induced Transition in the Lorenz System
Keyword(s):
AbstractWe 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.
2017 ◽
Vol 102
(5)
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pp. 1045-1055
2016 ◽
Vol 41
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pp. 84-103
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2019 ◽
Vol 29
(14)
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pp. 1950197
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1993 ◽
Vol 03
(04)
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pp. 1045-1049
2017 ◽
Vol 27
(08)
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pp. 1750128
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2021 ◽
Vol 31
(08)
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pp. 2130024