In this paper, a predator-prey model with Holling III type functional response is studied. It is interesting that the system is always uniformly persistent, which yields the existence of at least one positive periodic solutions for the corresponding periodic system. The result improves the corresponding ones in [11]. Moreover, an example is illustrated to verify the results by simulation.<\/p>\r\n","references":"[1] Z. Teng, On the persistence and positive periodic solution for planar\r\ncompeting Lotka-Volterra systems, Ann. of Diff. Eqs. 13 (1997) 275-286.\r\n[2] Z. Teng and L. Chen, Necessary and sufficient conditions for existence of\r\npositive periodic solutions of periodic predator-prey systems, Acta. Math.\r\nScientia 18 (1998) 402-406(in Chinese).\r\n[3] F. Chen, The permanence and global attractivity of Lotka-Volterra competition\r\nsystem with feedback controls, Nonlinear Anal.: RWA 7 (2006)\r\n133-143.\r\n[4] C. Egami, N. Hirano, Periodic solutions in a class of periodic delay\r\npredator-prey systems, Yokohama Math. J. 51(2004)45-61.\r\n[5] Z. Teng, Y. Yu, The stability of positive periodic solution for periodic\r\npredator-prey systems,Acta. Math. Appl. Sinica 21(1998)589-596.(in Chinese)\r\n[6] M. Fan, K. Wang, D. Jiang, Existence and global attractivity of positive\r\nperiodic solutions of periodic n-species Lotka-Volterra competition\r\nsystems with several deviating arguments, Math. Biosci. 160(1999)47-61.\r\n[7] F. Ayala, M. Gilpin and J. Etherenfeld, Competition between species:\r\ntheoretical systems and experiment tests, Theory Population Biol.\r\n4(1973)331-356.\r\n[8] M. Hassell, G. Varley, New inductive population model for insect parasites\r\nand its bearing on biological control, Nature 223(5211)(1969)1133-1137.\r\n[9] M. Hassell, Mutual Interference between Searching Insect Parasites, J.\r\nAnim. Ecol. 40(1971)473-486.\r\n[10] M. Hassell, Density dependence in single-species population, J. Anim.\r\nEcol. 44(1975)283-295.\r\n[11] X.Wang, Z. Du and J. Liang, Existence and global attractivity of positive\r\nperiodic solution to a Lotka-Volterra model, Nonlinear Anal.: RWA\r\ndoi: 10.1016\/j.nonrwa.2010.03.011\r\n[12] F. Chen, On a nonlinear nonautonomous predator-prey model with\r\ndiffusion and distributed delay, J. Comput. Appl. Math. 180 (2005) 33-49.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 44, 2010"}