Some remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains

Arnaud Ducrot; Vincent Guyonne; Michel Langlais

doi:10.3934/dcdss.2011.4.67

Article Contents

2011, Volume 4, Issue 1: 67-82. Doi: 10.3934/dcdss.2011.4.67

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Some remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains

1.
UMR CNRS 5251, I.M.B. and INRIA Bordeaux Sud-ouest Anubis, case 36, UFR Sciences et Modélisation, Université Victor Segalen Bordeaux 2, 3 ter, place de la Victoire - 33076 Bordeaux cedex
2.
INRIA Bordeaux Sud-ouest Anubis, case 36, Université Victor Segalen Bordeaux 2, 3 ter, place de la Victoire - 33076 Bordeaux cedex

Received: January 31, 2009

Revised: February 28, 2010

Published: January 2011

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Abstract

We are interested in the dynamical behaviour of the solution set to a two component reaction--diffusion system posed on non coincident spatial domains. The underlying biological problem is a predator--prey system featuring a non local numerical response to predation involving an integral kernel. Quite interesting while complex dynamics emerge from preliminary numerical simulations, driven both by diffusivities and by the parametric form or shape of the integral kernel. We consider a simplified version of this problem, with constant coefficients, and give some hints on the large time dynamics of solutions.

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Mathematics Subject Classification: Primary: 35K57, 35J25; Secondary: 92D25.

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References

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