zbMATH — the first resource for mathematics

Persistence in food chains with general interactions. (English) Zbl 0453.92017

92D40 Ecology
34D20 Stability of solutions to ordinary differential equations
Full Text: DOI
[1] Andronov, A.A.; Leontovich, E.A.; Gordon, I.I.; Maier, A.G., Qualitative theory of second order dynamical systems, (1973), Wiley New York · Zbl 0282.34022
[2] Gard, T.C., Persistence in food webs: Holling-type food chains, Math. biosci., 49, 61-67, (1980) · Zbl 0438.92019
[3] Gard, T.C.; Hallam, T.G., Persistence in food webs: I. Lotka-Volterra food chains, Bull. mathematical biology, 41, 877-891, (1979) · Zbl 0422.92017
[4] Goodman, D., The theory of diversity-stability relationships in ecology, Quart. rev. biol., 50, 237-266, (1975)
[5] Holling, C.S., Resilience and stability of ecological systems, Annu. rev. ecol. syst., 4, 1-23, (1973)
[6] May, R.M., Stability and complexity in model ecosystems, (1975), Princeton U.P Princeton, N.J
[7] Smith, J.Maynard, Models in ecology, (1974), University Press Cambridge · Zbl 0312.92001
[8] McGehee, R.; Armstrong, R.A., Some mathematical problems concerning the ecological problem of competitive exclusion, J. differential equations, 23, 30-52, (1977) · Zbl 0353.92007
[9] Paine, R.T., Food web complexity and species diversity, Amer. nat., 100, 65-75, (1966)
[10] So, J., A note on the global stability and bifurcation phenomenon of a Lotka-Volterra food chain, J. theoret. biol., 80, 185-187, (1979)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.