scholarly journals GLOBAL DYNAMICS OF AN AUTOCATALYTIC REACTION-DIFFUSION SYSTEM WITH FUNCTIONAL RESPONSE

2011 ◽  
Vol 1 (1) ◽  
pp. 121-142
Author(s):  
Yuncheng You ◽  
Keyword(s):  
Functional Response ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Autocatalytic Reaction ◽  
Global Dynamics

scholarly journals Complexity in a prey-predator model

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Baba I. Camara ◽  
Moulay A. Aziz Alaoui
Keyword(s):  
Functional Response ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Type Ii ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Réponse Fonctionnelle ◽  
International Audience ◽  
Predator Model

International audience In this paper we consider a predator-prey model given by a reaction-diffusion system. It incorporates the Holling-type-II and a modified Leslie-Gower functional response. We focus on qualitaive analysis, bifurcation mecanisms and patterns formation. Nous considérons un modèle proie-prédateur exprimé sous forme de système de réaction diffusion. En absence de diffusion, le système étudié est de type Holling-type-II et la réponse fonctionnelle une forme modifiée du terme de Leslie-Gower. Dans cet article, nous nous intéressons à l’analyse qualitative des solutions , l’étude des bifurcations et la formation de motifs spatio-temporels.

Analysis of a Delayed Predator-Prey Reaction-Diffusion System with Beddington-DeAngelis Functional Response and Two Stage Structure

2011 ◽  
Vol 204-210 ◽  
pp. 2065-2070
Author(s):  
Fang Wei Zhang ◽  
Shi He Xu ◽  
Bao Shi
Keyword(s):  
Functional Response ◽  
Upper And Lower Solutions ◽  
Reaction Diffusion ◽  
Stage Structure ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Mature Stage ◽  
Two Stage ◽  
Predator Prey ◽  
Positive Steady States

In this paper, we study a delayed predator-prey reaction-diffusion system with Beddington-DeAngelis functional response and two stage structure on prey, an immature and a mature stage. The time delays are the time lengths between the immature’s birth and maturity prey species. Under some simple assumptions, using upper and lower solutions method and a comparison principle we prove that the unique constant positive steady states solution is global asymptotic stability. The results shows that the dynamic behavior of solutions to this model is similar to that of solutions to corresponding model without diffusion.

Sign in / Sign up

Export Citation Format

Share Document