{"title":"Multiple Positive Periodic Solutions to a Periodic Predator-Prey-Chain Model with Harvesting Terms","authors":"Zhouhong Li, Jiming Yang","volume":56,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1292,"pagesEnd":1298,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/1330","abstract":"
In this paper, a class of predator-prey-chain model with harvesting terms are studied. By using Mawhin-s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient conditions are established for the existence of eight positive periodic solutions. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.<\/p>\r\n","references":"[1] Martino Bardi, Predator-prey models in periodically fluctuating environment,\r\nJ. Math. Biol. 12 (1981) 127-140.\r\n[2] Z. Zhang, Z. Wang, Periodic solution for a two-species nonautonomous\r\ncompetition Lotka-Volterra Patch system with time delay, J. Math. Anal.\r\nAppl. 265 (2002) 38-48.\r\n[3] Cushing, Two species competition in a periodic environment, J. Math.\r\nBiol. 10 (1980) 384-400.\r\n[4] L. Dong, L. Chen , A periodic predator-prey-chain system with impulsive\r\nperturbation, Journal of Computational and Applied Mathematics 223\r\n(2009) 578-584\r\n[5] K. Zhao, Y. Ye, Four positive periodic solutions to a periodic Lotka-\r\nVolterra predatory-prey system with harvesting terms, Nonlinear Anal.\r\nReal World Appl. 11 (2010) 2448-2455.\r\n[6] D. Hu, Z. Zhang, Four positive periodic solutions to a Lotka-Volterra\r\ncooperative system with harvesting terms, Nonlinear Anal. Real World\r\nAppl. 11 (2010) 1115-1121.\r\n[7] Y. Kuang, Delay Differential Equations With Applications in Population\r\nDynamics, Academic Press, Inc., 1993.\r\n[8] R. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differetial\r\nEquitions, Springer Verlag, Berlin, 1977.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 56, 2011"}