Periodicity in a Delayed Ratio-Dependent Predator–Prey System

Arditi, 1989, Coupling in predator–prey dynamics: Ratio-dependence, J. Theor. Biol, 139, 311, 10.1016/S0022-5193(89)80211-5 Arditi, 1991, Variation in plankton densities among lakes: A case for ratio-dependent models, Amer. Naturalist, 138, 1287, 10.1086/285286 Arditi, 1991, Functional response and heterogeneities: An experimental test with cladocerans, OIKOS, 60, 69, 10.2307/3544994 Arditi, 1992, Empirical evidence of the role of heterogeneity in ratio-dependent consumption, Ecology, 73, 1544, 10.2307/1940007 Beretta, 1998, Global analyses in some delayed ratio-dependent predator–prey systems, Nonlinear Anal., 32, 381, 10.1016/S0362-546X(97)00491-4 Cushing, 1977, 20 Gaines, 1977 Ginzburg, 1992, Consequences of ratio-dependent predation for steady state properties of ecosystems, Ecology, 73, 1536, 10.2307/1940006 Gutierrez, 1992, The physiological basis of ratio-dependent predator–prey theory: A metabolic pool model of Nicholson's blowflies as an example, Ecology, 73, 1552, 10.2307/1940008 Hanski, 1991, The functional response of predator: Worries about scale, TREE, 6, 141 Hsu, 1995, Global stability for a class of predator–prey systems, SIAM J. Appl. Math., 55, 763, 10.1137/S0036139993253201 Kuang, 1993, 191 Kuang, 1998, Global qualitative analysis of a ratio-dependent predator–prey system, J. Math. Biol, 36, 389, 10.1007/s002850050105 Li, 1999, Periodic solutions of a periodic delay predator–prey system, Proc. Amer. Math. Soc, 127, 1331, 10.1090/S0002-9939-99-05210-7 Sáez, 1999, Dynamics of a predator–prey model, SIAM J. Appl. Math., 59, 1867, 10.1137/S0036139997318457