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Mathematical analysis of some three-species food-chain models. (English) Zbl 0363.92022

92D25Population dynamics (general)
Full Text: DOI
[1] Albrecht, F.; Gatzke, H.; Haddad, A.; Wax, N.: The dynamics of two interacting populations. J. math. Anal. appl. 46, 658-670 (1974) · Zbl 0281.92012
[2] Andronov, A. A.; Leontovich, E. A.; Gordon, I. I.; Maier, A. G.: Qualitative theory of second-order dynamic systems. (1973) · Zbl 0282.34022
[3] Barclay, H.; Den Driessche, P. Van: Time lags in ecological systems. J. theor. Biol. 51, 347-356 (1975)
[4] Conrad, M.: Stability of foodwebs and its relation to species diversity. J. theor. Biol. 34, 325-335 (1972)
[5] De Angelis, D. L.: Stability and connectance in food web models. Ecology 56, 238-243 (1975)
[6] Freedman, H. I.: Graphical stability, enrichment, and pest control by a natural enemy. Math. biosci. 31, 207-225 (1976) · Zbl 0373.92023
[7] Freedman, H. I.; Waltman, P.: Perturbation of two-dimensional predator-prey equations. SIAM J. Appl. math. 28, 1-10 (1975) · Zbl 0313.92001
[8] 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
[9] Gallopin, G. C.: Trophic similarity between species in a food web. Am. midwest. Nat. 87, 336-345 (1972)
[10] Goel, N. S.; Maitra, S. C.; Montrol, E. W.: On the Volterra and other nonlinear models of interacting populations. Rev. mod. Phys. 43, 231-276 (1971)
[11] Hausrath, A. R.: Stability properties of a class of differential equations modeling predator-prey relationships. Math. biosci. 26, 267-281 (1975) · Zbl 0326.92001
[12] Haussman, U. G.: Abstract food webs in ecology. Math. biosci. 11, 291-316 (1971) · Zbl 0224.92019
[13] Haynes, D. L.; Sisojevic, P.: Predatory behavior of philodromus rufus walckenaer (Araneae: thomisidae). Can. entomol. 98, 113-133 (1966)
[14] Holling, C. S.: Some characteristics of simple types of predation and parasitism. Can. entomol. 91, 385-398 (1959)
[15] Hsu, S. B.: A mathematical analysis of competition for a single resource. Ph.d. thesis (1976)
[16] S.B. Hsu, S. Hubbell and P. Waltman, A mathematical theory for single-nutrient competition in continuous cultures of micro-organisms, SIAM J. Appl. Math., to be published. · Zbl 0354.92033
[17] Hubbell, S. P.: Populations and simple food webs as energy filters. I. one-species systems. Am. nat. 107, 94-121 (1973)
[18] Hubbell, S. P.: Populations and simple food webs as energy filters. II. two-species systems. Am. nat. 107, 122-151 (1973)
[19] Kerner, E. H.: On the Volterra-Lotka principle. Bull. math. Biophys. 23, 141-157 (1961) · Zbl 0124.36704
[20] May, R. M.: Stability and complexity in model ecosystems. (1973)
[21] May, R. M.: Mass and energy flow in closed ecosystems: a comment. J. theor. Biol. 39, 155-163 (1973)
[22] Smith, J. Maynard: Models in ecology. (1974) · Zbl 0312.92001
[23] Nemytskii, V. V.; Stepanov, V. V.: Qualitative theory of differential equations. (1960) · Zbl 0089.29502
[24] Rescigno, A.; Jones, K. G.: The struggle for life: III. A predator-prey chain. Bull. math. Biophys. 34, 521-532 (1972)
[25] Rosenzweig, M. L.: Exploitation in three tophic levels. Am. nat. 107, 275-294 (1973)
[26] Rosenzweig, M. L.; Macarthur, R. H.: Graphical representation and stability conditions of predator-prey interactions. Am. nat. 47, 209-223 (1963)
[27] Saunders, P. T.; Bazin, M. J.: On the stability of food chains. J. theor. Biol. 52, 121-142 (1975)
[28] Scudo, F. M.: Vito Volterra and theoretical ecology. Theoret. popul. Biol. 2, 1-23 (1971) · Zbl 0241.92001
[29] Yorke, J. A.; Jr., W. N. Anderson: Predator-prey patterns. Proc. nat. Acad. sci. USA 70, 2069-2071 (1973) · Zbl 0273.94028