Persistence and extinction in Lotka-Volterra reaction-diffusion equations

Linda J.S. Allen

doi:10.1016/0025-5564(83)90068-8

Persistence and extinction in Lotka-Volterra reaction-diffusion equations

Linda J.S. Allen

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

This paper analyzes the persistence and extinction behavior of Lotka-Volterra reaction-diffusion equations for a patch-type environment. The system of equations is the discretized version of the familiar random-diffusion model u_t=f(u)+Du_xx. It is shown that diffusion can alter the persistence or extinction behavior of the Lotka-Volterra system. A competitive or predator-prey system can become extinct, whereas a mutualistic system can persist.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Mathematical Biosciences
Volume	65
Issue number	1
DOIs	https://doi.org/10.1016/0025-5564(83)90068-8
State	Published - Jul 1983

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abstract = "This paper analyzes the persistence and extinction behavior of Lotka-Volterra reaction-diffusion equations for a patch-type environment. The system of equations is the discretized version of the familiar random-diffusion model ut=f(u)+Duxx. It is shown that diffusion can alter the persistence or extinction behavior of the Lotka-Volterra system. A competitive or predator-prey system can become extinct, whereas a mutualistic system can persist.",

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