Abstract
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.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference31 articles.
1. Benaïm, M.: Stochastic Persistence, pp. 1–82 (2018). arXiv e-prints arXiv:1806.08450
2. Bakhtin, Y., Hurth, T.: Invariant densities for dynamical systems with random switching. Nonlinearity 25(10), 2937–2952 (2012). https://doi.org/10.1088/0951-7715/25/10/2937
3. Bricmont, J., Kupiainen, A., Lefevere, R.: Ergodicity of the 2D Navier–Stokes equations with random forcing. Commun. Math. Phys. 224(1), 65–81 (2001). https://doi.org/10.1007/s002200100510
4. Brzeźniak, Z., Komorowski, T., Peszat, S.: Ergodicity for stochastic equation of Navier–Stokes type, pp. 1–13 (2020). arXiv e-prints arXiv:2003.08764
5. Bogachev, V.I.: Measure Theory, vol. I, II, Springer, Berlin (2007). https://doi.org/10.1007/978-3-540-34514-5
Cited by
9 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献