×

zbMATH — the first resource for mathematics

A criterion for permanent coexistence of species, with an application to a two-prey one-predator system. (English) Zbl 0524.92023

MSC:
92D40 Ecology
34C99 Qualitative theory for ordinary differential equations
92D25 Population dynamics (general)
34D99 Stability theory for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bhatia, N.P.; Szegö, G.P., (), 82
[2] Cramer, N.F.; May, R.M., Interspecific competition, predation and species diversity: a comment, J. theoret. biol., 34, 289-293, (1972)
[3] Fujii, K., Complexity-stability relationship of two-prey one-predator species system model: local and global stability, J. theoret. biol., 69, 613-623, (1977)
[4] Goh, B., Management and analysis of biological populations, (), 89
[5] Hofbauer, J., General cooperation theorem for hypercycles, Monatsh. math., 91, 233-240, (1981) · Zbl 0449.34039
[6] Hsu, S.B., Predator-mediated coexistence and extinction, Math. biosci., 54, 231-248, (1981) · Zbl 0456.92020
[7] Hutson, V.; Moran, W., Persistence of species obeying difference equations, J. theoret. biol., 15, 203-213, (1982) · Zbl 0495.92015
[8] (), 131-201
[9] May, R.M., Stability in multispecies community models, Math. biosci., 12, 59-79, (1971) · Zbl 0224.92006
[10] May, R.M., (), 58-62
[11] May, R.M.; Leonard, W.J., Nonlinear aspects of competition between three species, SIAM J. appl. math., 29, 243-253, (1975) · Zbl 0314.92008
[12] Parrish, J.D.; Saila, S.B., Interspecific competition, predation, and species diversity, J. theoret. biol., 27, 207-220, (1970)
[13] Schuster, P.; Sigmund, K.; Wolff, R., On ω-limits for competition between three species, SIAM J. appl. math., 37, 49-54, (1979) · Zbl 0418.92016
[14] Schuster, P.; Sigmund, K.; Wolff, R., Dynamical systems under constant organization. III. cooperative and competitive behaviour of hypercycles, J. differential equations, 32, 357-368, (1979) · Zbl 0384.34029
[15] Schuster, P.; Sigmund, K.; Hofbauer, J.; Wolff, R., Selfregulation of behaviour in animal societies, Biol. cybernet., 40, 1-8, (1981) · Zbl 0465.92016
[16] Vance, R.R., Predation and resource partitioning in one predator-two prey model communities, Amer. natur., 112, 797-813, (1978)
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.