Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 46, Issue 29, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/46/29/295002
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Funding
- Faculty of Engineering and Physical Sciences, University of Manchester
- EPSRC [EP/H02171X/1]
- EPSRC [EP/H02171X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/H02171X/1] Funding Source: researchfish
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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.
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