Continuous-time predator–prey systems with Allee effects in the prey

A continuous-time predator–prey model without spatial variation is proposed to study the impact of Allee effects upon the predator–prey interaction when the prey population is subject to Allee effects. The system exhibits a threshold below which both populations become extinct. The model undergoes a...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics and computers in simulation 2014-11, Vol.105, p.1-16
Main Authors: Aulisa, Eugenio, Jang, Sophia R.-J.
Format: Article
Language:English
Subjects:
Allee effects
Diffusion
Hopf bifurcation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A continuous-time predator–prey model without spatial variation is proposed to study the impact of Allee effects upon the predator–prey interaction when the prey population is subject to Allee effects. The system exhibits a threshold below which both populations become extinct. The model undergoes a Hopf bifurcation when the unique interior steady state loses its stability. We also examine the notion of Turing instability of the homogeneous interior steady state when both populations can disperse randomly. We prove that the solutions are square integrable and the system does not exhibit Turing instability. It is demonstrated via numerical simulations that the system may exhibit spatial nonhomogeneous steady states.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2014.04.004