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2014 Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species
Guohong Zhang, Xiaoli Wang
Abstr. Appl. Anal. 2014(SI06): 1-12 (2014). DOI: 10.1155/2014/167856

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.

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Guohong Zhang. Xiaoli Wang. "Effect of Diffusion and Cross-Diffusion in a Predator-Prey Model with a Transmissible Disease in the Predator Species." Abstr. Appl. Anal. 2014 (SI06) 1 - 12, 2014. https://doi.org/10.1155/2014/167856

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07021849
MathSciNet: MR3219356
Digital Object Identifier: 10.1155/2014/167856

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI06 • 2014
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