“…Numeric simulations of [3] show that the system has a globally stable fixed point and it is analytically verified, [4]. More work can be seen in [4][5][6][7][8][9].…”
Section: Introductionmentioning
confidence: 95%
“…Many other works in this direction are [5,[11][12][13][14][15]. Chen [16] has extended model (1.1a) by incorporating a refuge protecting mH of the prey, where m 2 ½0; 1Þ is constant.…”
“…Numeric simulations of [3] show that the system has a globally stable fixed point and it is analytically verified, [4]. More work can be seen in [4][5][6][7][8][9].…”
Section: Introductionmentioning
confidence: 95%
“…Many other works in this direction are [5,[11][12][13][14][15]. Chen [16] has extended model (1.1a) by incorporating a refuge protecting mH of the prey, where m 2 ½0; 1Þ is constant.…”
“…Yafia et al [27] studied the limit cycle bifurcated from time delay. For more works on Leslie-Gower predator-prey model, one could refer to [1], [4], [7], [8], [14], [26], [28], [29] and the references cited therein. To achieve further understanding it is now essential to consider more general and hence more "difficult" models.…”
Abstract-In this paper we study a predator-prey system, modeling the interaction of two species with diffusion and T -periodic environmental parameters. It is a Leslie-Gower type predator-prey model with Holling-type-II functional response. We establish some sufficient conditions for the ultimate boundedness of solutions and permanence of this system. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Numerical simulations are presented to illustrate the results.
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.
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