Yang, Wensheng; Li, Xuepeng Permanence for a delayed discrete ratio-dependent predator-prey model with monotonic functional responses. (English) Zbl 1167.34359 Nonlinear Anal., Real World Appl. 10, No. 2, 1068-1072 (2009). Summary: A delayed discrete ratio-dependent predator-prey model with monotonic functional responses is proposed. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system. Cited in 14 Documents MSC: 34D05 Asymptotic properties of solutions to ordinary differential equations 34K05 General theory of functional-differential equations 92D25 Population dynamics (general) 92D40 Ecology Keywords:predator-prey model; ratio-dependent; monotonic functional responses; permanence PDFBibTeX XMLCite \textit{W. Yang} and \textit{X. Li}, Nonlinear Anal., Real World Appl. 10, No. 2, 1068--1072 (2009; Zbl 1167.34359) Full Text: DOI References: [1] Fan, Y. H.; Li, W. T., Permanence in delayed ratio-dependent predator-prey models with monotonic functional responses, Nonlinear Anal., 8, 424-434 (2007) · Zbl 1152.34368 [2] Xu, C. Y.; Wang, M. J., Permanence for a delayed discrete three-level food-chain model with Beddington-DeAngelis functional response, Appl. Math. Comput., 187, 1109-1119 (2007) · Zbl 1120.92049 [3] Agarwal, R. P., Difference Equations and Inequalities: Theory, Method and Applications, Monographs and Textbooks in Pure and Applied Mathematics, vol. 228 (2000), Marcel Dekker: Marcel Dekker New York [4] Agarwal, R. P.; Wong, P. J.Y., Advance Topics in Difference Equations (1997), Kluwer Publisher: Kluwer Publisher Dordrecht · Zbl 0878.39001 [5] Freedman, H. I., Deterministic Mathematics Models in Population Ecology (1980), Marcel Dekker: Marcel Dekker New York · Zbl 0448.92023 [6] Murry, J. D., Mathematical Biology (1989), Springer-Verlag: Springer-Verlag New York [7] Gopalsamy, K., Stability and Oscillations in Delay Differential Equations of Population Dynamics (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Boston · Zbl 0752.34039 [8] Takeuchi, Y., Global Dynamical Properties of Lotka-Volterra Systems (1996), World Scientific Press · Zbl 0844.34006 [9] Wang, L.; Wang, M. Q., Ordinary Difference Equation (1991), Xinjiang University Press: Xinjiang University Press China, (in Chinese) [10] Chen, F. D., Permanence and global attractivity of a discrete multispecies Lotka-Volterra competition predator-prey systems, Appl. Math. Comput., 182, 3-12 (2006) · Zbl 1113.92061 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.