# Permanence and Extinction of a Diffusive Predator–Prey Model with Robin Boundary Conditions

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## Abstract

The main concern of this paper is to study the dynamic of a predator–prey system with diffusion. It incorporates the Holling-type-II and a modified Leslie–Gower functional responses under Robin boundary conditions. More concretely, we study the dissipativeness of the system by using the comparison principle, and we derive a criteria for permanence and for predator extinction.

## Keywords

Reaction–diffusion Robin boundary conditions Predator–prey Permanence Extinction## Mathematics Subject Classification

35B40 37N25## Notes

### Acknowledgements

This work was partially supported by the ERDF (XTerm Project) and Normandie Region, France. And also by The LMAH-FR-CNRS-3335.

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