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Zbl 1168.35377
Liu, Xiuxiang; Huang, Lihong
Permanence and periodic solutions for a diffusive ratio-dependent predator-prey system. (English)
[J] Appl. Math. Modelling 33, No. 2, 683-691 (2009). ISSN 0307-904X

Summary: This paper considers a diffusive predator-prey model, in which there is a ratio-dependent functional response with Holling III type. We establish some sufficient conditions for the ultimate boundedness of solutions and permanence of this system. The existence of a unique globally stable periodic solution is also presented.
MSC 2000:
*35K50 Systems of parabolic equations, boundary value problems
92D25 Population dynamics
35B10 Periodic solutions of PDE
35K57 Reaction-diffusion equations

Keywords: diffusive predator-prey system; functional response; permanence; periodic solutions; stability

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