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**On a delayed nonautonomous ratio-dependent predator-prey model with Holling type functional response and diffusion.**
*(English)*
Zbl 1193.34140

Summary: A two-species periodic ratio-dependent predator-prey model with Holling type functional response and diffusion is investigated. Three different sets of sufficient conditions (one set is diffusive independent and the other two sets are diffusive dependent) which ensure the permanence of the system and a set of sufficient condition which ensure the extinction of the predator species are obtained. Examples together with their numeric simulations show the feasibility of the main results.

### MSC:

34K13 | Periodic solutions to functional-differential equations |

34D05 | Asymptotic properties of solutions to ordinary differential equations |

92D25 | Population dynamics (general) |

### Keywords:

nonautonomous; diffusion; delay; predator-prey; permanence; Holling type functional response
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\textit{F. Chen} and \textit{J. Shi}, Appl. Math. Comput. 192, No. 2, 358--369 (2007; Zbl 1193.34140)

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### References:

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