Global dynamics of a lotka-volterra model with two predators competing for one prey

Jaume Llibre, Dongmei Xiao

Research output: Contribution to journalArticleResearchpeer-review

22 Citations (Scopus)

Abstract

In this paper, we study the global dynamics of a class of 3-dimensional Lotka-Volterra systems with eight parameters. This system describes two predators competing for the same food; i.e., they share one prey. By theoretical analysis on this system, we obtain sufficient and necessary conditions for the principle of competitive exclusion to hold and give the global dynamical behavior of the three species in the first octant. It is shown that there are two coexistence states for the three species: periodic oscillations and steady states, which depend on the resource for the prey. These results are biologically important in pest control. © 2014 Society for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)434-453
JournalSIAM Journal on Applied Mathematics
Volume74
Issue number2
DOIs
Publication statusPublished - 1 Jan 2014

Keywords

  • Coexistence
  • Extinction
  • Global dynamics
  • Lotka-Volterra model
  • Predator-prey

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