Influence of predation on species coexistence in Volterra models. (English) Zbl 0548.92014
This work is devoted to the study of the predator-mediated coexistence in some prey-predator Volterra models. Specifically the difference between the asymptotic behavior of a two-prey, one-predator and a two-prey, two- predator model is examined. There are found several results among which a significant one is that the stability of equilibria as well as the possibility of oscillatory coexistence increase with the inclusion of one or two predators.
Reviewer: G.Karakostas
MSC:
| 92D25 | Population dynamics (general) |
| 92D40 | Ecology |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34D99 | Stability theory for ordinary differential equations |
Keywords:
limit cycles; chaotic behaviors; global stability; bifurcation; predator- mediated coexistence; prey-predator Volterra models; stability of equilibria; oscillatory coexistenceReferences:
| [1] | Armstrong, R. A., The effects of connectivity on community stability, Amer. Natur., 120, 391-402 (1982) |
| [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] | Gilpin, M. E., Spiral chaos in a predator-prey model, Amer. Natur., 113, 306-308 (1979) |
| [5] | Goh, B. S., Sector stability of a complex ecosystem model, Math. Biosci., 40, 157-166 (1978) · Zbl 0386.92013 |
| [6] | Hsu, S. B., Predator-mediated coexistence and extinction, Math. Biosci., 54, 231-248 (1981) · Zbl 0456.92020 |
| [7] | Lubchenco, J., Plant species diversity in a marine intertidal community: Importance of herbivore food preference and algal competitive abilities, Amer. Natur., 112, 23-39 (1978) |
| [8] | Marsden, J. E.; McCraken, M., The Hopf Bifurcation and Its Application, ((1976), Springer: Springer Berlin), 131-135 · Zbl 0346.58007 |
| [9] | May, R. M., Stability in multispecies community models, Math. Biosci., 12, 59-79 (1971) · Zbl 0224.92006 |
| [10] | Paine, R. T., Food web complexity and species diversity, Amer. Natur., 100, 65-75 (1966) |
| [11] | Parrish, J. D.; Saila, S. B., Interspecific competition, predation, and species diversity, J. Theoret. Biol., 27, 207-220 (1970) |
| [12] | Takeuchi, Y.; Adachi, N., Existence and bifurcation of stable equilibrium in two-prey, one-predator communities, Bull. Math. Biol., 45, 877-900 (1983) · Zbl 0524.92025 |
| [13] | Vance, R. R., Predation and resource partitioning in one predator-two prey model communities, Amer. Natur., 112, 797-813 (1978) |
| [14] | Watt, K. E.F., Ecology and Resource Management (1968), McGraw-Hill: McGraw-Hill New York |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
