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Graphical stability, enrichment, and pest control by a natural enemy. (English) Zbl 0373.92023

MSC:
92D25 Population dynamics (general)
34D05 Asymptotic properties of solutions to ordinary differential equations
92B05 General biology and biomathematics
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[1] Ables, J.R.; Shepard, M., Responses and competition of the parasitoids spalangia endius and muscidifurax raptor (hymenoptera: pteromalidae) at different densities of house fly pupae, Can. entomol., 106, 825-830, (1974)
[2] Beddington, J.R., Mutual interference between parasites or predators and its effect on searching efficiency, J. anim. ecol., 44, 331-340, (1975)
[3] Beirne, B.P., Biological control attempts by introductions against pest insects in the field in Canada, Can. entomol., 107, 225-236, (1975)
[4] Bigger, M., An investigation by Fourier analysis into the interaction between coffee leaf-miners and their larval parasites, J. anim. ecol., 42, 417-434, (1973)
[5] Coddington, E.A.; Levinson, N., Theory of ordinary differential equations, (1970), McGraw-Hill New York · Zbl 0042.32602
[6] Diamond, P., The stability of the interaction between entomophagous parasites and their host, Math. biosci., 19, 121-129, (1974) · Zbl 0272.92006
[7] Ehler, L.E.; van den Bosch, R., An analysis of the natural biological control of trichoplusia ni (lepidoptera: noctuidae) on cotton in California, Can. entomol., 106, 1067-1073, (1974)
[8] Flaherty, D.L., Ecosystem complexity and densities of the willamette mite, eoletranychus willamettei ewing (acarina: tetranychidae), Ecology, 50, 911-916, (1969)
[9] Flaherty, D.L.; Huffaker, C.B., Biological control of Pacific mites and willamette mites in san joaquin valley vineyards: I. role of metaseiulus occidentalis, Hilgardia, 40, 267-308, (1970)
[10] Flaherty, D.L.; Huffaker, C.B., Biological control of Pacific mites and willamette mites in san joaquin valley vineyards: II. influence of dispersion patterns of metaseiulus occidentalis, Hilgardia, 40, 309-330, (1970)
[11] Freedman, H.I., A perturbed Kolmogorov-type model for the growth problem, Math. biosci., 23, 127-149, (1975) · Zbl 0321.92017
[12] H.I. Freedman, On a bifurcation theorem of Hopf and Friedrichs, to be published. · Zbl 0371.34027
[13] Freedman, H.I.; Waltman, P., Perturbation of two dimensional predator-prey equations, SIAM J. appl. math., 28, 1-10, (1975) · Zbl 0313.92001
[14] Freedman, H.I.; Waltman, P., Perturbation of two dimensional predator-prey equations with an unperturbed critical point, SIAM J. appl. math., 29, 719-733, (1975) · Zbl 0326.92002
[15] Friedrichs, K.O., Advanced ordinary differential equations, (1965), Gordon and Breach New York · Zbl 0191.38202
[16] Gause, G.F.; Smaragdova, N.P.; Witt, A.A., Further studies of interaction between predators and prey, J. anim. ecol., 5, 1-18, (1936)
[17] Ghabbour, S.I., Insecticides and cotton in Egypt, Biol. conserv., 5-6, 62-63, (1974)
[18] Gilpin, M.E., Enriched predator-prey systems: theoretical stability, Science, 177, 902-904, (1972)
[19] Goh, B.S.; Leitman, G.; Vincent, T.L., Optimal control of a prey-predator system, Math. biosci., 19, 263-286, (1974) · Zbl 0297.92013
[20] Hassell, M.P., A population model for the interaction between cyzenis albicans (fall.) (tachinidae) and operophtera brumata (L.) (geometridae) at wytham, berkshire, J. anim. ecol., 38, 567-576, (1969)
[21] Hassell, M.P.; Varley, G.C., New inductive population model for insect parasites and its bearing on biological control, Nature, 223, 1133-1137, (1969)
[22] Haynes, D.L.; Sisojevic, P., Predatory behavior of philodromus rufus walckenaer (araneae: thomisidae), Can. entomol., 98, 113-133, (1966)
[23] Holling, C.S., The components of predation as revealed by a study of small mammal predation of the European pine sawfly, Can. entomol., 91, 293-320, (1959)
[24] Holling, C.S., Some characteristics of simple types of predation and parasitism, Can. entomol., 91, 385-398, (1959)
[25] Holling, C.S., The tactics of a predator, Symp. R. entomol. soc. lond., 4, 47-58, (1968)
[26] Hopf, E., Abzweigung einer periodischer Lösung von einer stationären Lösung eines differential-systems, Ber. verh. Sächs. akad. wiss. leipz.-math.-nat. kl., 95, 3-22, (1943)
[27] Huffaker, C.B.; Kennett, C.E., Experimental studies on predation: predation and cyclamen-mite populations on strawberries in California, Hilgardia, 26, 191-222, (1956)
[28] Kolmogorov, A., Sulla teoria di Volterra Della lotta per l’essistenze, G. inst. ital. attuari, 7, 74-80, (1936) · JFM 62.1263.01
[29] Lotka, A.J., Elements of physical biology, (1925), Williams and Wilkins Baltimore · JFM 51.0416.06
[30] Matsumoto, B.M.; Huffaker, C.B., Regulatory processes and population cyclicity in laboratory populations of anagasta kuhniella (zeller) (lepidoptera: phycitidae) V. host finding and parasitization in a “small” universe by an entomophagous parasite, venturia canescens (gravenhorst) (hymenoptera: ichneumonidae), Res. popul. ecol., 15, 193-212, (1974)
[31] Matsumoto, B.M.; Huffaker, C.B., Regulatory processes and population cyclicity in laboratory populations of anagasta kuhneilla (zeller) (lepidoptera: phycitidae) VI. host finding and parasitization in a “large” universe by an entomophagous parasite, venturia canescens (gravenhorst) (hymenoptera: ichneumonidae), Res. popul. ecol., 15, 193-212, (1974)
[32] May, R.M., Stability and complexity in model ecosystems, (1973), Princeton U.P Princeton, N.J
[33] McAllister, C.D.; Le Brasseur, R.J.; Parsons, T.R., Stability of enriched acquatic ecosystems, Science, 175, 562-564, (1972)
[34] McMurtry, J.A.; van de Vrie, M., Predation by amblyseius potentillae (garman) on panonychus ulmi (Koch) in simple ecosystems (acarina: phytoseudae, tetranychidae), Hilgardia, 42, 17-34, (1973)
[35] Nicholson, A.J., The balance of animal populations, J. anim. ecol., 2, 132-178, (1933)
[36] Oaten, A.; Murdoch, W.W., Functional response and stability in predator-prey systems, Am. nat., 109, 289-298, (1975)
[37] Pimbley, G.H., Periodic solutions of predator-prey equations simulating an immune response, I, Math. biosci., 20, 27-51, (1974) · Zbl 0303.92006
[38] Pimbley, G.H., Periodic solutions of predator-prey equations simulating an immune response, II, Math. biosci., 21, 251-277, (1974) · Zbl 0301.92005
[39] Pimbley, G.H., Periodic solutions of third order predator-prey equations simulating an immune response, Arch. ration. mech. anal., 55, 93-123, (1974) · Zbl 0294.92002
[40] Polyakov, I.Ya., Ecological fundamentals of pest control in plants, Sov. J. ecol., 3, 305-314, (1972)
[41] Riebesell, J.F., Paradox of enrichment in competitive systems, Ecology, 55, 183-187, (1974)
[42] Rosenzweig, M.L., Why the prey curve has a hump, Am. nat., 103, 81-87, (1969)
[43] Rosenzweig, M.L., Paradox of enrichment: destabilization of exploitation ecosystems in ecological time, Science, 171, 385-387, (1971)
[44] Rosenzweig, M.L., Reply to mcallister et al.: “stability of enriched acquatic ecosystems”, Science, 175, 564-565, (1972)
[45] Rosenzweig, M.L., Reply to gilpin: “enriched predator-prey systems: theoretical stability”, Science, 177, 904, (1972)
[46] Rosenzweig, M.L., Evolution of the predator isocline, Evolution, 27, 84-94, (1973)
[47] Rosenzweig, M.L.; MacArther, R.H., Graphical representation and stability conditions of predator-prey interactions, Am. nat., 47, 209-223, (1963)
[48] Royama, T., A comparative study of models of predation and parasitism, Res. popul. ecol., 1-91, (1971), Supp. I
[49] Salt, G.W., Predation in an experimental protozoan population (woodruffia-paramecium), Ecol. monog., 37, 113-144, (1967)
[50] Salt, G.W.; Willard, D.E., The hunting behavior and success of Forster’s tern, Ecology, 52, 989-998, (1971)
[51] Schoener, T.W., Population growth regulated by intraspecific competition for energy or time: some simple representations, Theor. popul. biol., 4, 56-84, (1973) · Zbl 0281.92015
[52] Tanner, J.T., The stability and intrinsic growth rates of prey and predator populations, Ecology, 56, 855-867, (1975)
[53] Taylor, R.J., Role of learning in insect parasitism, Ecol. monogr., 44, 89-104, (1974)
[54] Volterra, V., Variazioni e fluttuazioni del numero d’individui in specie animali convivanti, Mem. R. com. talassogr. ital., 131, 1-142, (1927) · JFM 52.0450.06
[55] Wallace, M.M.H.; Walters, M.C., The introduction of bdellodes lapidaria (acari: bdellidae) from Australia into south africa for the biological control of sminthurus viridis (collembda), Aust. J. zool., 22, 505-517, (1974)
[56] Waltman, P.E., The equations of growth, Bull. math. biophys., 26, 39-43, (1964) · Zbl 0119.35802
[57] Watt, K.E.F., A mathematical model for the effect of densities of attached and attaching species on the number attacked, Can. entomol., 91, 129-144, (1959)
[58] Watt, K.E.F., Mathematical models for use in insect pest control, Can. entomol., 19, 1-62, (1961), (suppl.)
[59] Watt, K.E.F., Community stability and the strategy of biological control, Can. entomol., 97, 887-895, (1965)
[60] White, E.G.; Huffaker, C.B., Regulatory processes and population cyclicity in laboratory populations of anagasta kuhniella (zeller) (lepidoptera; phycitidae) II. parasitism, predation, competition and protective cover, Res. popul. ecol., 11, 150-155, (1969)
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