Rich dynamics of a ratio-dependent one-prey two-predators model

Sze Bi Hsu, Tzy Wei Hwang, Yang Kuang

Research output: Contribution to journalArticle

103 Citations (Scopus)

Abstract

The objective of this paper is to systematically study the qualitative properties of a ratio-dependent one-prey two-predator model. We show that the dynamics outcome of the interactions are very sensitive to parameter values and initial data. Specifically, we show the interactions can lead to all the following possible outcomes: 1) competitive exclusion; 2) total extinction, i.e., collapse of the whole system; 3) coexistence in the form of positive steady state; 4) coexistence in the form of oscillatory solutions; and 5) introducing a friendly and better competitor can save a otherwise doomed prey species. These results reveal far richer dynamics compared to similar prey dependent models. Biological implications of these results are discussed.

Original languageEnglish (US)
Pages (from-to)377-396
Number of pages20
JournalJournal of Mathematical Biology
Volume43
Issue number5
StatePublished - Nov 2001

Fingerprint

Ratio-dependent
Predator
Prey
predators
Coexistence
competitive exclusion
Competitive Exclusion
Oscillatory Solution
extinction
Qualitative Properties
Interaction
Extinction
Model
Dependent
Form

Keywords

  • Coexistence
  • Competitive exclusion
  • Extinction
  • Limit cycle
  • Ratio-dependent predator-prey model

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

Rich dynamics of a ratio-dependent one-prey two-predators model. / Hsu, Sze Bi; Hwang, Tzy Wei; Kuang, Yang.

In: Journal of Mathematical Biology, Vol. 43, No. 5, 11.2001, p. 377-396.

Research output: Contribution to journalArticle

Hsu, Sze Bi ; Hwang, Tzy Wei ; Kuang, Yang. / Rich dynamics of a ratio-dependent one-prey two-predators model. In: Journal of Mathematical Biology. 2001 ; Vol. 43, No. 5. pp. 377-396.
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