A noise-induced transition in the Lorenz system
arXiv:2004.12815 · doi:10.1007/s00220-021-04000-6
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.
Fixed a mathematical typo in Section 5
References in corpus (6)
- Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
- Spectral gaps in Wasserstein distances and the 2D stochastic Navier--Stokes equations
- Spectral Properties of Hypoelliptic Operators
- Invariant densities for dynamical systems with random switching
- How hot can a heat bath get?
- Randomly switched vector fields sharing a zero on a common invariant face