Dynamical Behaviors in a Discrete Predator-prey Model with a Prey Refuge
By incorporating a prey refuge, this paper proposes new discrete Leslie–Gower predator–prey systems with and without Allee effect. The existence of fixed points are established and the stability of fixed points are discussed by analyzing the modulus of characteristic roots.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070633Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1186
 Yongli Song, Sanling Yuan, Jianming Zhang. Bifurcation analysis in the delayed Leslie-Gower predator-prey system. Appl. Math. Modelling 33 (2009), 4049-4061.
 Eduardo Gonz'alez-Olivares, Rodrigo Ramos-Jiliberto. Dynamic consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability. Ecological Modelling 166 (2003), 135- 146.
 Liujuan Chen, Fengde Chen, Lijuan Chen. Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a constant prey refuge. Nonlinear Analysis: RWA 11 (2010), 246-252.
 Vlastimil K╦çrivan. Effects of Optimal Antipredator Behavior of Prey on PredatorCPrey Dynamics: The Role of Refuges. Theoretical Population Biology 53 (1998), 131-142.
 J.D. Murray. Mathematical Biology. New York: Springer-Verlag, 1989.
 R.P. Agarwal, P.J.Y. Wong. Advance Topics in Difference Equations. Dordrecht: Kluwer, 1997.
 Canan Celik, Oktay Duman. Allee effect in a discrete-time predator-prey system. Chaos, Solitons and Fractals 40 (2009), 1956-1962.
 P.H. Leslie. Some further notes on the use of matrices in population mathematics. Biometrika 35 (1948), 213-245.
 P.H. Leslie. A stochastic model for studying the properties of certain biological systems by numerical methods. Biometrika 45 (1958), 16-31.
 W. Ko, K. Ryu. Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge. Journal of Differential Equations 231 (2006), 534-550.
 T. Kumar Kar. Stability analysis of a prey-predator model incorporating a prey refuge. Communications in Nonlinear Science and Numeric Simulation 10 (2005), 681-691.
 Y. Huang, F. Chen, Z. Li. Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge. Applied Mathematics and Computation 182 (2006), 672-683.
 Xiaoli Liu, Dongmei Xiao. Complex dynamic behaviors of a discrete- time predator-prey system. Chaos, Solitons and Fractals 32 (2007), 80- 94.