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Liu, Zijian; Zhang, Lei; Bi, Ping; Pang, Jianhua; Li, Bing; Fang, Chengling

On the dynamics of one-prey-\(n\)-predator impulsive reaction-diffusion predator-prey system with ratio-dependent functional response. (English) Zbl 1447.92352

J. Biol. Dyn. 12, No. 1, 551-576 (2018).
Summary: In this paper, a one-prey-\(n\)-predator impulsive reaction-diffusion periodic predator-prey system with ratio-dependent functional response is investigated. On the basis of the upper and lower solution method and comparison theory of differential equation, sufficient conditions on the ultimate boundedness and permanence of the predator-prey system are established. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Examples and numerical simulations are presented to verify the feasibility of our results. A discussion is conducted at the end.

Cited in 2 Documents

MSC:

92D25 Population dynamics (general)
35K57 Reaction-diffusion equations
35B10 Periodic solutions to PDEs
35R12 Impulsive partial differential equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences

Keywords:

reaction-diffusion; ratio-dependent functional response; predator-prey system; permanence; stability
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References:

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