Demographic noise and piecewise deterministic Markov processes

TL;DR

This paper investigates how intrinsic demographic noise influences the behavior of piecewise deterministic Markov processes, especially in ecological systems, revealing noise-induced oscillations through analytical and numerical methods.

Contribution

It introduces a systematic approach to analyze demographic noise effects in hybrid systems using nonequilibrium statistical mechanics and system-size expansion techniques.

Findings

Demographic noise can induce oscillations in ecological systems.

Power spectrum analysis predicts noise-induced oscillations.

Analytical and numerical methods complement each other in studying system behavior.

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.