Dynamical Systems pp 165-178 | Cite as

# Competitive Exclusion by Zip Bifurcation

## Abstract

A model that describes the competition of two predator species for a single regenerating prey species was introduced by Hsu *et al.* (1978 a,b; see also Koch, 1974 a,b) and has been studied since then by several workers, e.g., Butler (1983), Keener (1983), Smith (1982), and Wilken (1982). In this model of a three-dimensional system of ordinary differential equations the prey population is assumed to have a logistic growth rate in the absence of predators, and the predator populations are assumed to obey a Holling-type functional response (Michaelis-Menten kinetics). Butler (1983) has shown that most of the results concerning the model of Hsu *et al.* can be achieved for a whole class of two-predator-one-prey models whose common feature is that the prey’s growth rate and the predators’ functional response are arbitrary functions satisfying certain natural conditions.

## Keywords

Hopf Bifurcation Invariant Manifold Predator Species Predator Population Natural Case## Preview

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## References

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