Zhang Yu Xuan, Rong Xin Miao, Zhang Ji Min
School of Mathematical Sciences, Heilongjiang University, 74 Xuefu Street, Harbin, Heilongjiang, 150080, P.R. China.
School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P.R. China.
Math Biosci Eng. 2019 Feb 21;16(3):1445-1470. doi: 10.3934/mbe.2019070.
This paper is devoted to exploring a diffusive predator-prey system with prey refuge and predator cannibalism. We investigate dynamics of this system, including dissipation and persistence, local and global stability of constant steady states, Turing instability, and nonexistence and existence of nonconstant steady state solutions. The influence of prey refuge and predator cannibalism on predator and prey biomass density is also considered by using a systematic sensitivity analysis. Our studies suggest that appropriate predator cannibalism has a positive effect on predator biomass density, and then high predator cannibalism may stabilize the predator-prey ecosystem and prevent the paradox of enrichment.
本文致力于探索一个具有猎物避难所和捕食者自相残杀的扩散捕食-食饵系统。我们研究该系统的动力学，包括耗散性和持久性、常数稳态的局部和全局稳定性、图灵不稳定性以及非常数稳态解的不存在性和存在性。还通过系统的敏感性分析考虑了猎物避难所和捕食者自相残杀对捕食者和猎物生物量密度的影响。我们的研究表明，适当的捕食者自相残杀对捕食者生物量密度有积极影响，进而高捕食者自相残杀可能会稳定捕食-食饵生态系统并防止富集悖论。
