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Constant-rate stocking of predator-prey systems. (English) Zbl 0448.92020

MSC:
92D25 Population dynamics (general)
92D40 Ecology
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
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[1] Bazykin, A. D.: Structure and dynamic stability of model predator-prey systems. Problems in mathematical genetics (V. A. Ratner, ed.), pp. 103-142, (USSR Acad. Sci., Novosibirsk) [English translation: Institute of Resource Ecology, University of British Columbia, Vancouver Research Report R-3-R] (1974)
[2] Brauer, F.: Boundedness of solutions of predator-prey systems. Theor. Popul. Biol. 15, 268-273 (1979) · Zbl 0399.92015 · doi:10.1016/0040-5809(79)90041-8
[3] Brauer, F., Soudack, A. C.: Stability regions and transition phenomena for harvested predator-prey systems. J. Math. Biol. 7, 319-337 (1979a) · Zbl 0397.92019 · doi:10.1007/BF00275152
[4] Brauer, F., Soudack, A. C.: Stability regions in predator-prey systems with constant-rate prey harvesting. J. Math. Biol. 8, 55-71 (1979b) · Zbl 0406.92020 · doi:10.1007/BF00280586
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[6] Clark, C.: Mathematical bioeconomics. New York: Wiley 1976 · Zbl 0364.90002
[7] Holling, C. S.: The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Ent. Soc. Canada 45, 1-73 (1965)
[8] Ivlev, V. S.: Experimental ecology of the feeding of fishes. New Haven: Yale University Press 1961
[9] Ludwig, D., Jones, D. S., Holling, C. S.: Qualitative analyses of insect outbreak systems: The spruce budworm and forest. J. Anim. Ecol. 47, 315-332 (1979) · doi:10.2307/3939
[10] May, R. M.: Stability and complexity in model ecosystems. Princeton: Princeton University Press 1973
[11] Maynard Smith, J.: Models in ecology. Cambridge: Cambridge University Press 1974 · Zbl 0312.92001
[12] O’Brien, W. J.: The dynamics of nutrient limitation of phytoplankton algae: A model reconsidered. Ecology 55, 135-141 (1974) · doi:10.2307/1934626
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