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A competition model for a seasonally fluctuating nutrient. (English) Zbl 0431.92027


MSC:

92D25 Population dynamics (general)
92D40 Ecology
34D20 Stability of solutions to ordinary differential equations
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References:

[1] Armstrong, R. A., McGehee, R.: Coexistence of species competing for shared resource. Theor. Pop. Biol. 9, 317-328 (1976) · Zbl 0349.92030 · doi:10.1016/0040-5809(76)90051-4
[2] Brauer, F.: Periodic solutions of some ecological models. J. Theor. Biol. 69, 143-152 (1977) · doi:10.1016/0022-5193(77)90392-7
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[4] Gradshteyn, I. S., Ryzhik, I. M.: Table of Integrals, Series and Products. New York and London: Academic Press 1965 · Zbl 0918.65002
[5] Hardin, G.: The competitive exclusion principle. Science 131, 1292-1298 (1960) · doi:10.1126/science.131.3409.1292
[6] Holling, C. S.: The functional response of predators to prey density and its role in mimicry and population regulation. Me. Entomol. Soc. Canada 45, 5-60 (1965)
[7] Holling, C. S.: The functional response of invertebrate predators to prey density. Mem. Entomol. Soc. Canada 48, 1-85 (1966)
[8] Hsu, S. B., Hubbell, S. P., Waltman, P. E.: A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms. Siam J. Appl. Math. 32, 366-383 (1977) · Zbl 0354.92033 · doi:10.1137/0132030
[9] Hsu, S. B.: Limiting behavior for competing species. Siam J. Appl. Math. 34, 760-763 (1978) · Zbl 0381.92014 · doi:10.1137/0134064
[10] McGehee, R., Armstrong, R. A.: Some mathematical problems concerning the ecological principle of competitive exclusion. J. Differential Equation 23, 30-52 (1977) · Zbl 0353.92007 · doi:10.1016/0022-0396(77)90135-8
[11] Stewart, F. M., Levin, B. R.: Partitioning of resources and the outcome of interspecific competition: a model and some general consideration. Amer. Nat. 7, 171-198 (1973) · doi:10.1086/282825
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