关联噪声驱动下多稳态系统中稀有事件的抑制
Mitigation of rare events in multistable systems driven by correlated noise
摘要：
我们考虑多稳态系统中色噪声激发引起的稀有跃迁。我们表明，不良的过渡可以减轻一个简单的时间延迟反馈控制，如果控制参数的明智选择。我们设计了一种用于选择最优控制参数的简约方法，而不需要对系统进行任何蒙特卡罗模拟。该方法依赖于一个新的非线性Fokker-Planck方程，其稳态响应分布由快速收敛的迭代算法近似。此外，我们的框架使我们能够准确地预测，并随后抑制，模态漂移和尾部膨胀的控制平稳分布。我们证明了我们的方法在两个例子，包括一个光学激光模型受乘性色噪声扰动的有效性。
英文摘要：
We consider rare transitions induced by colored noise excitation in multistable systems. We show that undesirable transitions can be mitigated by a simple time-delay feedback control if the control parameters are judiciously chosen. We devise a parsimonious method for selecting the optimal control parameters, without requiring any Monte Carlo simulations of the system. This method relies on a new nonlinear Fokker-Planck equation whose stationary response distribution is approximated by a rapidly convergent iterative algorithm. In addition, our framework allows us to accurately predict, and subsequently suppress, the modal drift and tail inflation in the controlled stationary distribution. We demonstrate the efficacy of our method on two examples, including an optical laser model perturbed by multiplicative colored noise.
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