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On global stability of a predator-prey system. (English) Zbl 0383.92014


MSC:

92D25 Population dynamics (general)
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[1] Andronov, A. A.; Leontovich, E. A.; Gordon, I. I.; Maier, A. G., Qualitative Theory of Second Order Dynamical Systems (1973), Wiley: Wiley New York · Zbl 0282.34022
[2] Freedman, H. I., Graphical stability, enrichment, and pest control by a natural enemy, Math. Biosci., 31, 207-225 (1976) · Zbl 0373.92023
[3] Gause, G. F.; Smaragdova, N. P.; Witt, A. A., Further studies of interaction between predators and prey, J. Anim. Ecol., 5, 1-18 (1936)
[4] Goh, B. S., Global stability in many species systems, Amer. Natur., III, 977, 135-143 (1977)
[5] Hsu, S. B., A mathematical analysis of competition for a single resource ph.D. Thesis (1976), University of Iowa
[6] Kolmogorov, A., Sulla teoria di Volterra della lotta per l’esistenze, Giorn. Ist. Ital. Attuari, 7, 74-80 (1936) · JFM 62.1263.01
[7] Labine, P. A.; Wilson, D. H., A teaching model of population interactions: an algae-daphnia-predator system, Bioscience, 23, 3, 162-167 (1973)
[8] LaSalle, J., Some extension of Lyapunov’s second method, IRE Trans. Circuit Theory, CT-7, 520-527 (1960)
[9] May, R. M., Stability and Complexity in Model Ecosystems (1974), Princeton U.P: Princeton U.P Princeton, N.J
[10] May, R. M., Theoretical Ecosystems (1976), Saunders
[11] Maynard Smith, J., Models in Ecology (1974), Cambridge · Zbl 0312.92001
[12] Oaten, A.; Murdoch, W. W., Functional response and stability in predator-prey systems, Amer. Natur., 109, 289-298 (1975)
[13] Rosenzweig, M. L., Why the prey curve has a hump, Amer. Natur., 103, 81-87 (1969)
[14] Rosenzweig, M. L.; MacArthur, R. H., Graphical representation and stability conditions of predator-prey interaction, Amer. Natur., 47, 209-223 (1963)
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