标题： 洛伦兹系统的噪声诱导过渡 显示英文标题

标题： A noise-induced transition in the Lorenz system

摘要： 我们研究了经典Lorenz系统的随机扰动，参数范围为原点是全局吸引子的情况。 我们证明，在最后一个分量中加入噪声会导致唯一遍历不变测度到恰好两个遍历不变测度的转变。 分歧阈值依赖于噪声的强度：如果噪声较弱，则唯一的不变测度是高斯测度，而足够强的噪声会引起第二个遍历不变测度的出现。 显示英文摘要

摘要： 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.