Effect of cross-diffusion in the diffusion prey-predator model with a protection zone II
Effect of cross-diffusion in the diffusion prey-predator model with a protection zone II
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DOI：
10.1016/j.jmaa.2017.12.029
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发表时间：
2017-12
影响因子：
1.3
通讯作者：
Shanbing Li;Yoshio Yamada
中科院分区：
文献类型：
--
作者：
Shanbing Li;Yoshio Yamada
在本文中，我们继续Li和Wu（2017）[15]和Oeda（2011）[22]中研究的数学分析，并进一步研究捕食者的交叉扩散对平稳问题的影响。首先利用分歧理论证明了正解的存在性。接下来我们讨论了当捕食种群的内禀增长率趋于无穷大时正解的极限行为。当预防系数趋于无穷大时，我们得到了两个阴影系统，并给出了正解的完全极限特征。
In the current paper, we continue the mathematical analysis studied inLi and Wu (2017)[15]andOeda (2011)[22], and further study the effect of cross-diffusion for the predator on the stationary problem. The existence of positive solutions is first established by the bifurcation theory. We next discuss the limiting behavior of positive solutions when the intrinsic growth rate of the predator species tends to infinity. Moreover, as the prevention coefficient tends to infinity, we obtain twoshadow systemsand give the complete limiting characterization of positive solutions.