We consider in this paper a microscopic model (that is, a system of three reaction–diffusion equations) incorporating the dynamics of handling and searching predators, and show that its solutions converge when a small parameter tends to 0 towards the solutions of a reaction–cross diffusion system of predator–prey type involving a Holling-type II or Beddington–DeAngelis functional response. We also provide a study of the Turing instability domain of the obtained equations and (in the case of the Beddington–DeAngelis functional response) compare it to the same instability domain when the cross diffusion is replaced by a standard diffusion.

About reaction–diffusion systems involving the Holling-type II and the Beddington–DeAngelis functional responses for predator–prey models

Conforto, F.
Primo
;
2018

Abstract

We consider in this paper a microscopic model (that is, a system of three reaction–diffusion equations) incorporating the dynamics of handling and searching predators, and show that its solutions converge when a small parameter tends to 0 towards the solutions of a reaction–cross diffusion system of predator–prey type involving a Holling-type II or Beddington–DeAngelis functional response. We also provide a study of the Turing instability domain of the obtained equations and (in the case of the Beddington–DeAngelis functional response) compare it to the same instability domain when the cross diffusion is replaced by a standard diffusion.
File in questo prodotto:
File Dimensione Formato  
2018_CDS_NoDEA_online.pdf

solo gestori archivio

Descrizione: Articolo principale
Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 821.73 kB
Formato Adobe PDF
821.73 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3133696
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 13
  • ???jsp.display-item.citation.isi??? 8
social impact