Differential and Integral Equations

A mathematical analysis of a predator-prey system in a highly heterogeneous environment

B'E Ainseba, F. Heiser, and M. Langlais

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Abstract

We are concerned with the mathematical analysis of a predator--prey system in heterogeneous domains. We first give a global existence result for the problem with spatially variable coefficients. For highly heterogeneous systems, using homogenization techniques we derive a simpler model with constant coefficients yielding the macroscopic dynamic of the predator--prey system. In this process, standard Lotka--Volterra functional responses to predation are preserved, while Holling type II responses are transformed into unusual nonlocal nonlinearities.

Article information

Source
Differential Integral Equations, Volume 15, Number 4 (2002), 385-404.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060842

Mathematical Reviews number (MathSciNet)
MR1870419

Zentralblatt MATH identifier
1011.35075

Subjects
Primary: 35K57: Reaction-diffusion equations
Secondary: 35B35: Stability 35B40: Asymptotic behavior of solutions 35K40: Second-order parabolic systems 92D25: Population dynamics (general) 92D40: Ecology

Citation

Ainseba, B'E; Heiser, F.; Langlais, M. A mathematical analysis of a predator-prey system in a highly heterogeneous environment. Differential Integral Equations 15 (2002), no. 4, 385--404. https://projecteuclid.org/euclid.die/1356060842


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