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Some results on global stability of a predator-prey system. (English) Zbl 0464.92021

92D25Population dynamics (general)
Full Text: DOI
[1] Albrecht, F., Gatzke, H., Haddad, A., Wax, N.: The dynamics of two interacting populations. J. Math. Anal. Appl. 46, 658-670 (1974) · Zbl 0281.92012 · doi:10.1016/0022-247X(74)90267-4
[2] Freedman, H. I.: Graphical stability, enrichment, and pest control by a natural enemy. Math. Biosci. 31, 207-225 (1976) · Zbl 0373.92023 · doi:10.1016/0025-5564(76)90080-8
[3] Gaus, G. F., Smaragdova, N. P., Witt, A. A.: Further studies of interaction between predators and prey. J. Anim. Ecol. 5, 1-18 (1936) · doi:10.2307/1087
[4] Goh, B. S.: Global stability in many species systems. Amer. Natur. 111 (977), 135-143 (1977) · doi:10.1086/283144
[5] Hale, J. K.: Ordinary differential equations. New York: Wiley-Interscience 1969 · Zbl 0186.40901
[6] Hastings, A.: Global stability of two species system. J. Math. Biol. 5, 399-403 (1978) · Zbl 0382.92008
[7] Hsu, S. B.: On global stability of a predator-prey system. Math. Biosci. 39, 1-10 (1978) · Zbl 0383.92014 · doi:10.1016/0025-5564(78)90025-1
[8] Hsu, S. B., Hubbel, S. P., Waltman, P.: Competing predators. SIAM J. Applied Math. 35, 617-625 (1978) · Zbl 0394.92025 · doi:10.1137/0135051
[9] May, R. M.: Stability and complexity in model ecosystems. Princeton, U.P., Princeton, N.J., 1974
[10] Oaten, A., Murdoch, W. W.: Functional response and stability in predator-prey system. Amer. Natur. 109, 289-298 (1975) · doi:10.1086/282998
[11] Real, L. A.: The kinetics of functional response. Amer. Natur. 111 (1978), 289-300 (1977)
[12] Rosenzweig, M. L.: Why the prey curve has a hump. Amer. Natur. 103, 81-87 (1969) · doi:10.1086/282584
[13] Rosenzweig, M. L., MacArthur, R. H.: Graphical representation and stability conditions of predator-prey interaction. Amer. Natur. 97, 209-223 (1963) · doi:10.1086/282272
[14] Rosenzweig, M. L.: Paradox of enrichment: Destabilization of exploitation ecosystem in ecological time. Science 171, 385-387 (1971) · doi:10.1126/science.171.3969.385
[15] Maynard Smith, J.: Models in ecology. Cambridge: University Press 1974