Stochastic dynamics on slow manifolds

George W A Constable, Alan J. McKane, Tim Rogers

    Research output: Contribution to journalArticlepeer-review

    Abstract

    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 paper 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. © 2013 IOP Publishing Ltd.
    Original languageEnglish
    Article number295002
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume46
    Issue number29
    DOIs
    Publication statusPublished - 26 Jul 2013

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