退化阻尼随机Lorenz系统定态的灵敏度
Sensitivity of steady states in a degenerately-damped stochastic Lorenz system
摘要：
本文研究了Lorenz '63模型的随机驱动和退化阻尼解的稳定性。具体地说，我们证明了当阻尼是不存在的温度分量之一，系统具有唯一不变的概率测度当且仅当噪声作用于对流变量。另一方面，如果有一个积极的增长项的垂直温度分布，我们证明了没有归一化不变的状态。我们的方法依赖于非平凡的李雅普诺夫函数的推导和分析，以确保积极的复发或零复发/瞬态的动态。
英文摘要：
We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant probability measure if and only if noise acts on the convection variable. On the other hand, if there is a positive growth term on the vertical temperature profile, we prove that there is no normalizable invariant state. Our approach relies on the derivation and analysis of non-trivial Lyapunov functions which ensure positive recurrence or null-recurrence/transience of the dynamics.
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