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hal-00541302, version 1

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

Arnaud Ducrot () 1, 2, Vincent Guyonne () 2, Michel Langlais () 1, 2

discrete and continuous Dynamical Systems series S 4, 1 (2011) 67-82

  • 1:  Institut de Mathématiques de Bordeaux (IMB)
  • http://www.math.u-bordeaux.fr/IMB/
    CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II 351 cours de la Libération 33405 TALENCE CEDEX France
  • 2:  ANUBIS (INRIA Bordeaux - Sud-Ouest)

  • INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR France

Bibliographic reference

  • Type of document: Articles in peer-reviewed journal
  • Subject:
    Mathematics/Analysis of PDEs
    Life Sciences/Ecology, environment/Ecosystems
  • Title: Some remarks on the qualitative properties of solutions to a predator–prey model posed on non coincident spatial domains
  • Abstract: We are interested in the dynamical behaviour of the solution set to a two component reaction–diffusion system posed on non coincident spatial do- mains. 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 simu- lations, 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.
  • Fulltext language: English
  • Production date: 2009-02
  • DOI: 10.3934/dcdss.2011.4.67
  • Journal: discrete and continuous Dynamical Systems series S
  • Audience: international
  • Publication date: 2011-02
  • Volume: 4
  • Issue: 1
  • Page, identifiant, ...: 67-82
  • Keyword(s): Reaction-Diffusion system – non-coincident spatial domains – stationary solutions – degree theory – persistence
  • Classification: Primary: 35K57, 35J25; Secondary: 92D25
 
  • hal-00541302, version 1
  • http://hal.archives-ouvertes.fr/hal-00541302
  • oai:hal.archives-ouvertes.fr:hal-00541302
  • From: Michel Langlais <>
  • Submitted on: Tuesday, 30 November 2010 12:21:26
  • Updated on: Tuesday, 30 November 2010 12:21:26