论文标题
洛伦兹系统中的噪声引起的过渡
A noise-induced transition in the Lorenz system
论文作者
论文摘要
我们考虑经典洛伦兹系统的随机扰动，在该参数范围内，该参数是全局吸引子。我们表明，在最后一个组件中添加噪声会导致从唯一到两个千古不变的度量的过渡。分叉阈值取决于噪声的强度：如果噪声很弱，唯一不变的度量是高斯，而足够强的噪声会导致第二次千古不变的度量的出现。
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.
