A discrete-time model with non-monotonic functional response and strong Allee effect in prey

Ziyad AlSharawi, Saheb Pal, Nikhil Pal, Joydev Chattopadhyay*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we investigate the impact of strong Allee effect on the stability of a discrete-time predator–prey model with a non-monotonic functional response. The dynamics of discrete-time predator–prey models with strong Allee effect is studied earlier. But, the mathematical investigations of predator–prey dynamics in discrete-time set up with Holling type-IV functional response and strong Allee effect in prey are lacking. The proposed model supports the coexistence of two steady states, and the mathematical features of the model are analyzed based on local stability and bifurcation theory. By considering the Allee parameter as the bifurcation parameter, we provide sufficient conditions for the flip and the Neimark–Sacker bifurcations. We observe that Allee parameter plays a significant role in the dynamics of the system.

Original languageEnglish
Pages (from-to)404-431
Number of pages28
JournalJournal of Difference Equations and Applications
Volume26
Issue number3
DOIs
Publication statusPublished - Mar 3 2020
Externally publishedYes

Keywords

  • Allee effect
  • bistability
  • flip bifurcation
  • local stability
  • Neimark–Sacker bifurcation
  • Predator–prey model

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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