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Stability regions and transition phenomena for harvested predator-prey systems. (English) Zbl 0397.92019

92D25Population dynamics (general)
Full Text: DOI
[1] Albrecht, F., Gatzke, H., Haddad, A., Wax, N.: The dynamics of two interacting populations. J. Math. Analysis and Appl. 46, 658-670 (1974) · Zbl 0281.92012 · doi:10.1016/0022-247X(74)90267-4
[2] Brauer, F.: Destabilization of predator-prey systems under enrichment. Int. J. Control 23, 541-552 (1976) · Zbl 0319.92012 · doi:10.1080/00207177608922180
[3] Brauer, F.: Boundedness of solutions of predator-prey systems. Theor. Pop. Biol. to appear, 1979 · Zbl 0399.92015
[4] Brauer, F., Soudack, A. C., Jarosch, H. S.: Stabilization, and destabilization of predator-prey systems under harvesting and nutrient enrichment. Int. J. Control 23, 553-573 (1976) · Zbl 0317.92003 · doi:10.1080/00207177608922181
[5] Bulmer, M. G.: The theory of prey-predator oscillations. Theor. Pop. Biol. 9, 137-150 (1976) · Zbl 0352.92015 · doi:10.1016/0040-5809(76)90041-1
[6] Coddington, E. A., Levinson, N.: Theory of Ordinary Differential Equations. New York: McGraw-Hill, 1955 · Zbl 0064.33002
[7] Conley, C. C.: Isolated Invariant Sets and the Morse Index. Conference Board on Mathematical Sciences, 1978 · Zbl 0397.34056
[8] Holling, C. S.: The functional response of predators to prey density and its rate in mimicry and population regulation. Mem. Ent. Soc. Canada 45, 1-73 (1965)
[9] Kolmogorov, A. N.: Sulla teoria di Volterra della lotta per l’esistenza. Giorn. Inst. Ital. Attuari 7, 74-80 (1936) · Zbl 62.1263.01
[10] Kopell, N., Howard, L. N.: Bifurcations and trajectories joining critical points. Adv. in Math. 18, 306-358 (1975) · Zbl 0361.34026 · doi:10.1016/0001-8708(75)90048-1
[11] Ludwig, D., Jones, D. S., Holling, C. S.: Qualitative analyses of insect outbreak systems: The spruce budworm and forest. J. Animal Ecology 47, 315-332 (1978) · doi:10.2307/3939
[12] May, R. M.: Stability and Complexity in Model Ecosystems. Princeton: Princeton Univ. Press, 1973
[13] Thom, R.: Structural Stability and Morphogenesis. Reading, Mass.: W. A. Benjamin, 1975 · Zbl 0303.92002