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A diffusive predator-prey system with prey refuge and predator cannibalism

1 School of Mathematical Sciences, Heilongjiang University, 74 Xuefu Street, Harbin, Heilongjiang, 150080, P.R. China
2 School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P.R. China
3 Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin, Heilongjiang, 150080, P.R. China

Special Issues: Modeling and Complex Dynamics of Populations

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.
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Keywords predator-prey system; predator cannibalism; prey refuge; steady states; stability

Citation: Yuxuan Zhang, Xinmiao Rong, Jimin Zhang. A diffusive predator-prey system with prey refuge and predator cannibalism. Mathematical Biosciences and Engineering, 2019, 16(3): 1445-1470. doi: 10.3934/mbe.2019070


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