Effect of Diffusion and Cross‐Diffusion in a Predator‐Prey Model with a Transmissible Disease in the Predator Species

Guohong Zhang and Xiaoli Wang

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2014/167856

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:167856

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().