论文标题
在退化的随机洛伦兹系统中稳态的敏感性
Sensitivity of steady states in a degenerately-damped stochastic Lorenz system
论文作者
论文摘要
我们研究了解决方案的稳定性，用于洛伦兹'63模型的随机驱动和退化的版本。具体而言，我们证明，当一个温度组件之一中缺乏阻尼时，当噪声作用于对流变量上时，系统具有独特的不变概率度量。另一方面，如果在垂直温度曲线上存在正增长项，我们证明没有可正常化的状态。我们的方法依赖于非平凡的lyapunov函数的推导和分析，这些函数可确保动力学的正复发或无效/瞬时/瞬时。
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.
