Bifurcations in a discrete predator–prey model with nonmonotonic functional response

Jicai Huang, Sanhong Liu, Shigui Ruan, Dongmei Xiao

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

The predator–prey/consumer–resource interaction is the most fundamental and important process in population dynamics. Many species, such as monocarpic plants and semelparous animals, have discrete nonoverlapping generations and their births occur in regular breeding seasons. Their interactions are described by difference equations or formulated as discrete-time mappings. In this paper we study bifurcations in a discrete predator–prey model with nonmonotone functional response described by a simplified Holling IV function. It is shown that the model exhibits various bifurcations of codimension 1, including fold bifurcation, transcritical bifurcation, flip bifurcations and Neimark–Sacker bifurcation, as the values of parameters vary. Moreover, we establish the existence of Bogdanov–Takens bifurcation of codimension 2 and calculate the approximate expressions of bifurcation curves. Numerical simulations are also presented to illustrate the theoretical analysis. These results demonstrate that the Bogdanov–Takens bifurcation of codimension 2 at the degenerate singularity persists in all three versions of the predator–prey model with nonmonotone functional response: continuous-time, time-delayed, and discrete-time.

Original languageEnglish (US)
JournalJournal of Mathematical Analysis and Applications
DOIs
StateAccepted/In press - Jan 1 2018

Keywords

  • Bogdanov–Takens bifurcation
  • Discrete predator–prey model
  • Flip bifurcations
  • Fold bifurcation
  • Neimark–Sacker bifurcation
  • Transcritical bifurcation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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