Yaying Dong, Shanbing Li, Yanling Li
Abstract:
This article concerns the stationary problem of a cross-diffusion
prey-predator system with a protection zone for the prey.
We first give the necessary condition and sufficient condition
for the existence of coexistence states of the two species,
by applying the bifurcation theory. Furthermore, the asymptotic
behavior of coexistence states is established as the cross-diffusion
coefficient of the prey tends to infinity. We also analyze the
corresponding limiting system.
Submitted March 15, 2018. Published March 22, 2019.
Math Subject Classifications: 35J65, 35B32, 92D25.
Key Words: Prey-predator model; cross-diffusion; protection zone; stationary.
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Yaying Dong School of Science Xi'an Polytechnic University Xi'an 710048, China. email: dongyaying@xpu.edu.cn |
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| Shanbing Li School of Mathematics and Statistics Xidian University Xi'an, 710071, China email: lishanbing@xidian.edu.cn | |
| Yanling Li College of Mathematics and Information Science Shaanxi Normal University Xi'an, 710062, China email: yanlingl@snnu.edu.cn |
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