Electron. J. Differential Equations, Vol. 2019 (2019), No. 44, pp. 1-14.

Effects of cross-diffusion for a prey-predator system in a heterogeneous environment

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.
email: dongyaying@xpu.edu.cn
  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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