Complex dynamic behaviors of a discrete-time predator–prey system
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Verhulst, 1838, Notice sur la loi que la population suit dans son accroissement, Corr Math Phys, 10, 113
Pearl, 1920, On the rate of growth of the population of the United States since 1790 and its mathematical representation, Proc Natl Acad Sci, 6, 275, 10.1073/pnas.6.6.275
Brauer, 2001
Freedman, 1980
Murray, 1993
Strogatz, 1994
May, 1974, Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos, Science, 186, 645, 10.1126/science.186.4164.645
May, 1976, Simple mathematical models with very complicated dynamics, Nature, 261, 459, 10.1038/261459a0
Summers, 2000, Chaos in periodically forced discrete-time ecosystem models, Chaos, Solitons & Fractals, 11, 2331, 10.1016/S0960-0779(99)00154-X
Gao, 2004, Chaos and bifurcation in the space-clamped FitzHugh–Nagumo system, Chaos, Solitons & Fractals, 21, 943, 10.1016/j.chaos.2003.12.033
Jing, 2002, Chaos behavior in the discrete BVP oscillator, Int J Bifurcat & Chaos, 12, 619, 10.1142/S0218127402004577
Jing, 2004, Bifurcation and chaos in discrete FitzHugh–Nagumo system, Chaos, Solitons & Fractals, 21, 701, 10.1016/j.chaos.2003.12.043
Rosenzweig, 1963, Graphical representation and stability conditions of predator–prey interactions, Amer Naturalist, 97, 209, 10.1086/282272
Beddington, 1975, Dynamic complexity in predator–prey models framed in difference equations, Nature, 255, 58, 10.1038/255058a0
Lopez-Ruiz, 2005, Indirect Allee effect, bistability and chaotic oscillations in a predator–prey discrete model of logistic type, Chaos, Solitons & Fractals, 24, 85, 10.1016/j.chaos.2004.07.018
Xiao, 2002, Dynamic complexities in predator–prey ecosystem models with age-structure for predator, Chaos, Solitons & Fractals, 14, 1403, 10.1016/S0960-0779(02)00061-9
Fan, 2002, Periodic solutions of a discrete time non-autonomous ratio-dependent predator–prey system, Math Comput Model, 35, 951, 10.1016/S0895-7177(02)00062-6
Wang, 1999, Global stability of discrete models of Lotka–Volterra type, Nonlinear Anal, 35, 1019, 10.1016/S0362-546X(98)00112-6
Huo, 2004, Stable periodic solution of the discrete periodic Leslie–Gower predator–prey model, Math Comput Model, 40, 261, 10.1016/j.mcm.2004.02.026
Robinson, 1999
Guckenheimer, 1983