Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment

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Abstract

A two-species ratio-dependent predator-prey diffusion model with time delay is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are obtained for the local and global stability of the positive equilibrium of the system.

Keywords

Time delay
Diffusion
Uniform persistence
Global asymptotic stability

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The authors would like to thank the referee for his/her many valuable comments and helpful suggestions that improved the presentation of this work.