Stability and bifurcation analysis of a delayed predator–prey model of prey dispersal in two-patch environments
Tài liệu tham khảo
Hassard, 1981
Ruan, 2003, On the zero of some transcendental functions with applications to stability of delay differential equations with two delays, Dyn. Contin. Discrete Impuls. Syst. Ser. A, 10, 863
Yang, 1993
Hale, 1977
L.J. Chen, Permanence for a delayed predator–prey model of prey dispersal in two-patch environments, J. Appl. Math. Comput., doi:10.1007/S12190-009-0317-7.
Sun, 2006, Stability and Hopf bifurcation for an epidemic disease model with delay, Chaos Solitons Fract., 30, 204, 10.1016/j.chaos.2005.08.167
Kuang, 1994, Predator–prey dynamics in models of prey dispersal in two-patch environments, Math. Biosci., 120, 77, 10.1016/0025-5564(94)90038-8
Takeuchi, 2006, Permanence of dispersal population model with time delays, J. Comput. Appl. Math., 192, 417, 10.1016/j.cam.2005.06.002
Xu, 2004, Periodic solutions for a delayed predator–prey model of prey dispersal in two-patch environments, Nonlinear Anal.: Real World Appl., 5, 183, 10.1016/S1468-1218(03)00032-4
Zhou, 2008, Analysis of non-autonomous predator–prey model with nonlinear diffusion and time delay, Appl. Math. Comput., 196, 129, 10.1016/j.amc.2007.05.041
Chen, 2005, On a nonlinear non-autonomous predator–prey model with diffusion and distributed delay, J. Comput. Appl. Math., 180, 33, 10.1016/j.cam.2004.10.001
Chen, 2006, Permanence and extinction in nonlinear single and multiple species system with diffusion, Appl. Math. Comput., 177, 410, 10.1016/j.amc.2005.11.019
Sun, 2007, Global stability for an special SEIR epidemic model with nonlinear incidence rates, Chaos Solitons Fract., 33, 290, 10.1016/j.chaos.2005.12.028
Hale, 1993
Li, 2004, Global stability of an SEI epidemic model, Chaos Solitons Fract., 21, 925, 10.1016/j.chaos.2003.12.031
Li, 2005, Global stability of an SEI epidemic model with general contact rate, Chaos Solitons Fract., 23, 997
Gao, 2008, Hopf bifurcation and global stability for a delayed predator–prey system with stage structure for predator, Appl. Math. Comput., 202, 721, 10.1016/j.amc.2008.03.011
Xu, 2008, Stability and Hopf bifurcation in a ratio-dependent predator–prey system with stage structure, Chaos Solitons Fract., 38, 669, 10.1016/j.chaos.2007.01.019
Hethcote, 2000, The mathematics of infectious diseases, SIAM Rev., 42, 599, 10.1137/S0036144500371907
Beretta, 1997, Convergence results in SIR epidemic model with varying populations sizes, Nonlinear Anal., 28, 1909, 10.1016/S0362-546X(96)00035-1
Shulgin, 1998, Pulse vaccination strategy in the SIR epidemic model, Bull. Math. Biol., 60, 1, 10.1016/S0092-8240(98)90005-2
