title: Model reduction for slow-fast stochastic systems with metastable behaviour.
abstract: The quasi-steady-state approximation (or stochastic averaging principle) is a useful tool in the study of multiscale stochastic systems, giving a practical method by which to reduce the number of degrees of freedom in a model. The method is extended here to slow-fast systems in which the fast variables exhibit metastable behaviour. The key parameter that determines the form of the reduced model is the ratio of the timescale for the switching of the fast variables between metastable states to the timescale for the evolution of the slow variables. The method is illustrated with two examples: one from biochemistry (a fast-species-mediated chemical switch coupled to a slower varying species), and one from ecology (a predator-prey system). Numerical simulations of each model reduction are compared with those of the full system.
authors.affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
authors.forename: Maria
authors.initials: M
authors.lastname: Bruna
authors.affiliation: Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
authors.forename: S Jonathan
authors.initials: SJ
authors.lastname: Chapman
authors.affiliation: Computational Science Laboratory, Microsoft Research, Cambridge CB1 2FB, United Kingdom.
authors.forename: Matthew J
authors.initials: MJ
authors.lastname: Smith
mesh_terms: D000465:Algorithms; D004463:Ecology; D020387:Food Chain; D007700:Kinetics; D008956:Models, Chemical; D013269:Stochastic Processes