A noise-induced transition in the Lorenz system
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910987520573440 |
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| author | Zelati, Michele Coti Hairer, Martin |
| author_facet | Zelati, Michele Coti Hairer, Martin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_12815 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A noise-induced transition in the Lorenz system Zelati, Michele Coti Hairer, Martin Probability Classical Analysis and ODEs Dynamical Systems 60H10, 37H20 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. |
| title | A noise-induced transition in the Lorenz system |
| topic | Probability Classical Analysis and ODEs Dynamical Systems 60H10, 37H20 |
| url | https://arxiv.org/abs/2004.12815 |