Yaying Dong, Shanbing Li, Yanling Li
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.
| Shanbing Li |
School of Mathematics and Statistics
Xi'an, 710071, China
|Yanling Li |
College of Mathematics and Information Science
Shaanxi Normal University
Xi'an, 710062, China
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