title: Demographic noise and piecewise deterministic Markov processes.
abstract: We explore a class of hybrid (piecewise deterministic) systems characterized by a large number of individuals inhabiting an environment whose state is described by a set of continuous variables. We use analytical and numerical methods from nonequilibrium statistical mechanics to study the influence that intrinsic noise has on the qualitative behavior of the system. We discuss the application of these concepts to the case of semiarid ecosystems. Using a system-size expansion we calculate the power spectrum of the fluctuations in the system. This predicts the existence of noise-induced oscillations.
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom. john.realpegomez@manchester.ac.uk
authors.forename: John
authors.initials: J
authors.lastname: Realpe-Gomez
authors.forename: Tobias
authors.initials: T
authors.lastname: Galla
authors.forename: Alan J
authors.initials: AJ
authors.lastname: McKane
mesh_terms: D000818:Animals; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D011157:Population Dynamics