zbMATH — the first resource for mathematics

Convergence of ecological competition between two species. (English) Zbl 0725.92025
We consider a two-species system in which the first species would fare better in the absence of the second and the second is dependent on the first as it is to survive. That is, we are dealing with two species host parasite systems in which the parasite depends for subsistence on a single species of host and can not turn to an alternative food source.
We give a method for the convergence of the solutions of the prey- predator competitive system with a set of sufficient conditions. The theory of ecological competition modelled by the system in this paper is neither specific about the resource of the prey competed for nor specific about how the prey acquire and utilize the resources.

92D40 Ecology
34E99 Asymptotic theory for ordinary differential equations
Full Text: DOI
[1] Ayala, F.J; Gilpin, M.E; Ehrenfeld, J.G, Competition between species; theoretical models and experimental tests, Theoret. population biol., 4, 331-356, (1973)
[2] Gilpin, M.E; Ayala, F.J, Global models of growth and competition, (), 3590-3593 · Zbl 0272.92016
[3] Gopalaswamy, K, Time lags and global stability in two species competition, Bull. math. biol., 42, 728-737, (1980) · Zbl 0453.92014
[4] Pielou, E.C, An introduction to mathematical ecology, (1969), Wiley-Interscience New York · Zbl 0259.92001
[5] Schoener, W.T, Alternatives to Lotka-Volterra competition; models of intermediate complexity, Theoret. population biol., 10, 309-333, (1976) · Zbl 0352.92016
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.