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[1]XU R. Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response [J]. Nonlinear Dyn, 2012, 67: 1683-1693.[2]DENG L W, WANG X D, PENG M. Hopf bifurcation analysis for a ratio-dependent predator-prey system with two delays and stage structure for the predator [J].Applied Mathematics and Computation, 2014, 231: 214-230.[3]WANG L, FAN Y, LI W. Multiple bifurcations in a predator-prey system with monotonic functional response [J]. Applied Mathematics and Computation, 2006, 172: 1103-1120.[4]XIAO D M , RUAN S G. Multiple bifurcation in a delayed predator-prey system with nonmonotonic functional response [J]. Journal of Differential Equations, 2001, 176: 494-510.[5]XIA J, LIU Z, YUAN R, et al. The effects of harvesting and time delay on predator-prey systems with Holling type II functional response [J]. SIAM J Appl Math, 2009, 70: 1178-1200.[6]JIANG J, SONG Y L. Delay-induced Bogdanov-Takens bifurcation in a Leslie-Gower predator-prey model with nonmonotonic functional response [J].Commun Nonlinear Sci Numer Simulat, 2014, 19: 2454-2465.[7] CAMPBELL S A, YUAN Y. Zero singularities of codimension two and three in delay differential equations [J]. Nonlinearity, 2008, 21:2671-2691.[8] GUO S J, MAN J J. Center manifolds theorem for parameterized delay differential equations with applications to zero singularities [J]. Nonlinear Analysis, 2011, 74: 4418-4432.[9] QIAO Z Q, LIU X B, ZHU D M. Bifurcation in delay differential systems with triple-zero singularity [J]. Chinese Ann Math Ser A, 2010, 31:59-70.[10] FARIA T, MAGALH widetilde A ES L T. Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity [J]. Journal of Differential Equations, 1995, 122:201-224.[11] CHOW S N, LI C Z, WANG D. Normal Forms and Bifurcation of Planar Vector Fields [M]. Cambridge: Cambridge University Press, 1994.
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