**Volume 17, Issue 2, pp 266-277**

**Publication Date**: 2017-06-15

http://dx.doi.org/10.22436/jmcs.017.02.08

Fengde Chen - College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian, 350002, P. R. China.

Qiaoxia Lin - College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian, 350002, P. R. China.

Xiangdong Xie - Department of Mathematics, Ningde Normal University, Ningde, Fujian, 352300, P. R. China.

Yalong Xue - Department of Mathematics, Ningde Normal University, Ningde, Fujian, 352300, P. R. China.

A nonautonomous modified Leslie-Gower predator-prey model with Holling-type III schemes and a prey refuge is proposed and studied in this paper. Sufficient conditions which guarantee the permanence and global stability of the system are obtained, respectively. Our results indicate that the prey refuge has no influence on the persistent property of the system, while it has positive effect on the stability property of the system. Numeric simulations show the feasibility of the main results.

Predator, prey, permanence, global stability.

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