Global dynamics of a predator-prey model

Xiuxiang Liu, Yijun Lou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


This paper deals with the dynamics of a predator-prey model with Hassell-Varley-Holling functional response. First, we show that the predator coexists with prey if and only if predator's growth ability is greater than its death rate. Second, using a blow-up technique, we prove that the origin equilibrium point is repelling and extinction of both predator and prey populations is impossible. Third, the local and global stability of the positive steady state coincide when the predator interference is large. Finally, for a typical biological case, we show instability of the positive equilibrium implies global stability of the limit cycle. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.
Original languageEnglish
Pages (from-to)323-340
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 Nov 2010
Externally publishedYes


  • Coexistence and extinction
  • Complicated equilibrium
  • Global stability
  • Predator-dependent response
  • Predator-prey model
  • Uniqueness of limit cycles

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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