Permanence and periodic solutions for a diffusive ratio-dependent predator-prey system. (English) Zbl 1168.35377

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.


35K50 Systems of parabolic equations, boundary value problems (MSC2000)
92D25 Population dynamics (general)
35B10 Periodic solutions to PDEs
35K57 Reaction-diffusion equations
Full Text: DOI


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