Stochastic dynamics on slow manifolds

George W A Constable, Alan J McKane, Tim Rogers

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17 Citations (Scopus)
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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.
Original languageEnglish
Article number295002
JournalJournal of Physics A: Mathematical and Theoretical
Volume46
Issue number29
DOIs
Publication statusPublished - 26 Jul 2013

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Slow Manifold
Stochastic Dynamics
dynamical systems
Dynamical systems
epidemiology
Stochastic Dynamical Systems
ecology
Epidemiology
Analytical Approximation
Ecology
simplification
Simplification
degrees of freedom
Dynamical system
Degree of freedom
Trajectories
trajectories
Model
methodology
Trajectory

Cite this

Stochastic dynamics on slow manifolds. / Constable, George W A; McKane, Alan J; Rogers, Tim.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 29, 295002, 26.07.2013.

Research output: Contribution to journalArticle

Constable, George W A ; McKane, Alan J ; Rogers, Tim. / Stochastic dynamics on slow manifolds. In: Journal of Physics A: Mathematical and Theoretical. 2013 ; Vol. 46, No. 29.
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