Bifurcation analysis in a predator–prey system with a functional response increasing in both predator and prey densities

Kimun Ryu, Wonlyul Ko, Mainul Haque

Research output: Journal PublicationArticlepeer-review

21 Citations (Scopus)

Abstract

This paper presents a qualitative study of a predator–prey interaction system with the functional response proposed by Cosner et al. (Theor Popul Biol 56:65–75, 1999). The response describes a behavioral mechanism which a group of predators foraging in linear formation searches, contacts and then hunts a school of prey. On account of the response, strong Allee effects are induced in predators. In the system, we determine the existence of all feasible nonnegative equilibria; further, we investigate the stabilities and types of the equilibria. We observe the bistability and paradoxical phenomena induced by the behavior of a parameter. Moreover, we mathematically prove that the saddle-node, Hopf and Bogdanov–Takens types of bifurcations can take place at some positive equilibrium. We also provide numerical simulations to support the obtained results.

Original languageEnglish
Pages (from-to)1639-1656
Number of pages18
JournalNonlinear Dynamics
Volume94
Issue number3
DOIs
Publication statusPublished - 1 Nov 2018
Externally publishedYes

Keywords

  • Allee effect
  • Bistability
  • Bogdanov–Takens
  • Hopf bifurcation
  • Predator–prey
  • Saddle-node

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering

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