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

92D25Population dynamics (general)
Full Text: DOI
[1] Andronov, A. A.; Leontovich, E. A.; Gordon, I. I.; Maier, A. G.: Qualitative theory of second order dynamical systems. (1973) · 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. 3, No. 977, 135-143 (1977)
[5] Hsu, S. B.: A mathematical analysis of competition for a single resource ph.d. Thesis. (1976)
[6] Kolmogorov, A.: Sulla teoria di Volterra Della lotta per l’esistenze. Giorn. ist. Ital. attuari 7, 74-80 (1936)
[7] Labine, P. A.; Wilson, D. H.: A teaching model of population interactions: an algae-daphnia-predator system. Bioscience 23, No. 3, 162-167 (1973)
[8] Lasalle, J.: Some extension of Lyapunov’s second method. IRE trans. Circuit theory 7, 520-527 (1960)
[9] May, R. M.: Stability and complexity in model ecosystems. (1974)
[10] May, R. M.: Theoretical ecosystems. (1976)
[11] Smith, J. Maynard: Models in ecology. (1974) · 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)