Effect of diffusion and cross-diffusion in a predator-prey model with a transmissible disease in the predator species
type: Item
instance of: scholarly article
title: Effect of diffusion and cross-diffusion in a predator-prey model with a transmissible disease in the predator species
zbMATH Open document ID: 1406.92537
DOI: 10.1155/2014/167856
author: Guohong Zhang
author: Xiaoli Wang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We study a Lotka-Volterra type predator-prey model with a transmissible disease in the predator population. We concentrate on the effect of diffusion and cross-diffusion on the emergence of stationary patterns. We first show that both self-diffusion and cross-diffusion can not cause Turing instability from the disease-free equilibria. Then we find that the endemic equilibrium remains linearly stable for the reaction diffusion system without cross-diffusion, while it becomes linearly unstable when cross-diffusion also plays a role in the reaction-diffusion system; hence, the instability is driven solely from the effect of cross-diffusion. Furthermore, we derive some results for the existence and nonexistence of nonconstant stationary solutions when the diffusion rate of a certain species is small or large.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 7021849
zbMATH Keywords: predator-prey model
zbMATH Keywords: transmissible disease in predator
zbMATH Keywords: cross-diffusion
Wikidata QID: Q59035673
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/167856
OpenAlex ID: W2080307515
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description: scientific article; zbMATH DE number 7021849