Stability and bifurcation analysis of a discrete predator–prey model with nonmonotonic functional response

Nonlinear Analysis: Real World Applications - Tập 12 - Trang 2356-2377 - 2011
Zengyun Hu1, Zhidong Teng1, Long Zhang1
1College of Mathematics and Model Sciences, Xinjiang University, Urumqi 830046, People’s Republic of China

Tài liệu tham khảo

Gao, 2005, The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulse, Chaos Solitons Fractals, 24, 1013, 10.1016/j.chaos.2004.09.091

Beretta, 2002, Nonexistence of periodic solutions in delayed Lotka–Volterra systems, Nonlinear Anal., 3, 107, 10.1016/S1468-1218(01)00017-7

Teng, 2002, Nonautonomous Lotka–Volterra systems with delays, J. Differential Equations, 179, 538, 10.1006/jdeq.2001.4044

Redheffer, 1996, Nonautonomous Lotka–Volterra systems, I, J. Differential Equations, 127, 519, 10.1006/jdeq.1996.0081

Teng, 2000, On the non-autonomous Lotka–Volterra N-species competing systems, Appl. Math. Comput., 114, 175, 10.1016/S0096-3003(99)00110-1

Wang, 2001, Global stability of discrete population models with time delays and fluctuating environment, J. Math. Anal. Appl., 264, 147, 10.1006/jmaa.2001.7666

Huo, 2004, Permanence and global stability for nonautonomous discrete model of Plankton Allelpathy, Appl. Math. Lett., 17, 1007, 10.1016/j.aml.2004.07.002

Dai, 2006, Permanence for the Michaelis–Menten type discrete three-species ratio-dependent food chain model with delay, J. Math. Anal. Appl., 324, 728, 10.1016/j.jmaa.2005.12.060

Wang, 1999, Global stability of discrete models of Lotka–Volterra type, Nonlinear Anal., 35, 1019

Saito, 2001, A necessary and sufficeint condition for permanence of a Lotka–Volterra discrete system with delays, J. Math. Anal. Appl., 256, 162, 10.1006/jmaa.2000.7303

Liao, 2007, On permanence and global stability in a general Gilpin–Ayala competition predator–prey discrete system, Appl. Math. Comput., 190, 500, 10.1016/j.amc.2007.01.041

Teng, 2003, Permanence and extinction of periodic predator–prey systems in a patchy environment with delay, Nonlinear Anal., 4, 335, 10.1016/S1468-1218(02)00026-3

Song, 2009, Bifurction analysis in the delayed Leslie–Gower predator–prey system, Appl. Math. Model., 33, 4049, 10.1016/j.apm.2009.02.008

Boukal, 2007, How predator functional responses and allee effects in prey affect the paradox of enrichment and population collapses, Theor. Popul. Biol., 72, 136, 10.1016/j.tpb.2006.12.003

Kar, 2009, Stability and bifurcation of a prey–predator model with time delay, C. R. Biol., 332, 642, 10.1016/j.crvi.2009.02.002

Lian, 2009, Hopf bifurcation analysis of a predator–prey system with holling IV functional response and time delay, Appl. Math. Comput., 215, 1484, 10.1016/j.amc.2009.07.003

Xu, 2010, Stability and bifurcation analysis of a delayed predator–prey model of prey disperal in two patch environments, Appl. Math. Comput., 216, 2920, 10.1016/j.amc.2010.04.004

Xiao, 2006, Dynamics in a ratio-dependent predator–prey model with predator harvesting, J. Math. Anal. Appl., 324, 14, 10.1016/j.jmaa.2005.11.048

Liu, 2007, Complex dynamic behaviors of a discrete-time predator–prey system, Chaos Solitons Fractals, 32, 80, 10.1016/j.chaos.2005.10.081

Agiza, 2009, Chaotic dynamics of a discrete prey–predator model with holling type II, Nonliear Anal., 10, 116, 10.1016/j.nonrwa.2007.08.029

Celik, 2009, Allee effect in a discrete-time predator–prey system, Chaos Solitons Fractals, 40, 1956, 10.1016/j.chaos.2007.09.077

Ruan, 2001, Global analysis in a predator–prey system with nonmonotonic functional response, SIAM J. Appl. Math., 61, 1445, 10.1137/S0036139999361896

C. Robinson, Dynamical Models, Stability, Symbolic Dynamics and Chaos, 2nd ed., London, New York, Washington, DC, Boca Raton, 1999.

Guckenheimer, 1983

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Nonlinear Analysis: Real World Applications

Tập 12

2356-2377

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