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December 2016 Lotka–Volterra with randomly fluctuating environments or “how switching between beneficial environments can make survival harder”
Michel Benaïm, Claude Lobry
Ann. Appl. Probab. 26(6): 3754-3785 (December 2016). DOI: 10.1214/16-AAP1192

Abstract

We consider two-dimensional Lotka–Volterra systems in a fluctuating environment. Relying on recent results on stochastic persistence and piecewise deterministic Markov processes, we show that random switching between two environments that are both favorable to the same species can lead to the extinction of this species or coexistence of the two competing species.

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Michel Benaïm. Claude Lobry. "Lotka–Volterra with randomly fluctuating environments or “how switching between beneficial environments can make survival harder”." Ann. Appl. Probab. 26 (6) 3754 - 3785, December 2016. https://doi.org/10.1214/16-AAP1192

Information

Received: 1 October 2015; Revised: 1 February 2016; Published: December 2016
First available in Project Euclid: 15 December 2016

zbMATH: 1358.92075
MathSciNet: MR3582817
Digital Object Identifier: 10.1214/16-AAP1192

Subjects:
Primary: 34A60 , 60J99

Keywords: competitive exclusion , Markov processes , Persistence , piecewise deterministic processes , Population dynamics

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 2016
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