慢流形上的随机动力学
Stochastic dynamics on slow manifolds
摘要：
慢流形理论是研究确定性动力系统的一个重要工具，它提供了一种减少模型中相关自由度的实用方法，从而往往导致相当大的简化。在这篇文章中，我们演示了如何相同的基本方法也可以应用到随机动力系统，通过检查的行为轨迹的条件下，他们不离开慢流形的事件。我们将该方法应用于两个模型：一个从生态学和一个从流行病学，实现了模型维数的减少，并说明了高质量的分析近似。
英文摘要：
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable simplification. In this article we demonstrate how the same basic methodology may also be applied to stochastic dynamical systems, by examining the behaviour of trajectories conditioned on the event that they do not depart the slow manifold. We apply the method to two models: one from ecology and one from epidemiology, achieving a reduction in model dimension and illustrating the high quality of the analytical approximations.
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