{"title":"Dynamics of a Discrete Three Species Food Chain System","authors":"Kejun Zhuang, Zhaohui Wen","volume":51,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":260,"pagesEnd":263,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/11767","abstract":"<p>The main purpose of this paper is to investigate a discrete time three&ndash;species food chain system with ratio dependence. By employing coincidence degree theory and analysis techniques, sufficient conditions for existence of periodic solutions are established.<\/p>\r\n","references":"[1] Haifeng Huo, Wantong Li, J J Nieto. Periodic solutions of delayed\r\npredator-prey model with the Beddington-DeAngelis functional response.\r\nChaos, Solitons and Fractals, 33(2007), 505-512.\r\n[2] Changyong Xu, Meijuan Wang. Permanence for a delayed discrete three-\r\nlevel food-chain model with Beddington-DeAngelis functional response.\r\nApplied Mathematics and Computation, 187(2007), 1109-1119.\r\n[3] A. Maiti, A.K. Pal, G.P. Samanta. Effect of time-delay on a food chain\r\nmodel. Applied Mathematics and Computation, 200(2008), 189-203.\r\n[4] Chengjun Sun, Michel Loreau. Dynamics of a three-species food chain\r\nmodel with adaptive traits. Chaos, Solitons and Fractals, 41(2009), 2812-\r\n2819.\r\n[5] Zhijun Zeng. Dynamics of a non-autonomous ratio-dependent food chain\r\nmodel. Applied Mathematics and Computation, 215(2009), 1274-1287.\r\n[6] Raid Kamel Naji, Ranjit Kumar Upadhyay, Vikas Rai. Dynamical consequences\r\nof predator interference in a tri-trophic model food chain.\r\nNonlinear Analysis: Real World Applications, 11(2010), 809-818.\r\n[7] Fengyan Wang, Guoping Pang. Chaos and Hopf bifurcation of a hybrid\r\nratio-dependent three species food chain. Chaos, Solitons and Fractals,\r\n(36)2008, 1366-1376.\r\n[8] Pingzhou Liu, K. Gopalsamy. Global stability and chaos in a population\r\nmodel with piecewise constant arguments. Applied Mathematics and\r\nComputation, 101(1999), 63-88.\r\n[9] Bingbing Zhang, Meng Fan. A remark on the application of coincidence\r\ndegree to periodicity of dynamic equtions on time scales. J. Northeast\r\nNormal University(Natural Science Edition), 39(2007), 1-3.(in Chinese)\r\n[10] R E Gaines, J L Mawhin. Coincidence Degree and Nonlinear Differential\r\nEquations. Lecture Notes in Mathematics, Berlin: Springer-Verlag, 1977.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 51, 2011"}