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.

11 pages, 5 figures, minor changes

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Cited by in corpus (5)

• Intrinsic noise in systems with switching environments
• Demographic noise and resilience in a semi-arid ecosystem model
• Strongly degenerate time inhomogeneous SDEs: densities and support properties. Application to a Hodgkin-Huxley system with periodic input
• Scaling analysis of time series of daily prices from stock markets of transitional economies in the Western Balkans
• Transition densities for strongly degenerate time inhomogeneous random models