A noise-induced transition in the Lorenz system

2020/04/27 by Zelati, Michele Coti, Hairer, Martin · 2 citations
#37H20 #60H10 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.12815

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.

Cited by

• Synchronization by degenerate noise
• Quasi-Gaussianity of the 2D stochastic Navier-Stokes equations

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