Billings Lora, Schwartz Ira B
Department of Mathematical Sciences, Montclair State University, Montclair, New Jersey 07043, USA.
Chaos. 2008 Jun;18(2):023122. doi: 10.1063/1.2929748.
We consider the approximation of fluctuation induced almost invariant sets arising from stochastic dynamical systems. The dynamical evolution of densities is derived from the stochastic Frobenius-Perron operator. Given a stochastic kernel with a known distribution, approximate almost invariant sets are found by translating the problem into an eigenvalue problem derived from reversible Markov processes. Analytic and computational examples of the methods are used to illustrate the technique, and are shown to reveal the probability transport between almost invariant sets in nonlinear stochastic systems. Both small and large noise cases are considered.
我们考虑由随机动力系统产生的涨落诱导的几乎不变集的逼近。密度的动力学演化由随机弗罗贝尼乌斯 - 佩龙算子导出。给定具有已知分布的随机核，通过将问题转化为从可逆马尔可夫过程导出的特征值问题来找到近似几乎不变集。该方法的解析和计算示例用于说明该技术，并展示了非线性随机系统中几乎不变集之间的概率转移。同时考虑了小噪声和大噪声情况。
