effect of diffusion and cross-diffusion in a predator-prey model with a transmissible disease in the predator species
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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.
| Reference Key |
zhang2014abstracteffect
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|---|---|
| Authors | ;Guohong Zhang;Xiaoli Wang |
| Journal | science and technology of advanced materials |
| Year | 2014 |
| DOI |
10.1155/2014/167856
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