effect of diffusion and cross-diffusion in a predator-prey model with a transmissible disease in the predator species

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ID: 247346
2014
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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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zhang2014abstracteffect Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Guohong Zhang, Xiaoli Wang
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Journal science and technology of advanced materials
Year 2014
DOI
10.1155/2014/167856
URL
http://dx.doi.org/10.1155/2014/167856
Keywords
mathematics

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