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A noise-induced transition in the Lorenz system (2004.12815v4)
Published 27 Apr 2020 in math.PR, math.CA, and math.DS
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.