Dynamics of a predator-prey model with discrete and distributed delay
type: Item
instance of: scholarly article
title: Dynamics of a predator-prey model with discrete and distributed delay
zbMATH Open document ID: 1474.37125
DOI: 10.1504/IJDSDE.2020.111483
author: Bootan Rahman
author: Muhammad A. Yau
author: K. B. Blyuss
author: Y. N. Kyrychko
published in: International Journal of Dynamical Systems and Differential Equations
publication date: 2021-05-07T00:00:00Z
review text: Summary: This paper considers a predator-prey model with discrete time delay representing prey handling time and assumed equal to the predator maturation period, and a distributed time delay describing intra-species interactions. We show that due to the delayed logistic growth of the prey, it is impossible for the species to become extinct through predation. Conditions for existence and local stability of the co-existence equilibrium are derived in terms of system parameters. Using techniques of centre manifold reduction and the normal form theory, we establish the direction of Hopf bifurcation of the co-existence equilibrium, as well as the stability of the bifurcating period solution. Numerical bifurcation analysis and simulations are performed to illustrate regions of stability of the co-existence equilibrium, to investigate how the amplitude and the period of bifurcating periodic solutions depend on parameters, and to demonstrate different types of dynamics of the system.
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 7345598
zbMATH Keywords: stability
zbMATH Keywords: discrete and distributed delay
zbMATH Keywords: predator-prey model
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: periodic solutions
Wikidata QID: Q113236842
MaRDI profile type: Publication
full work available at URL: ijdsde.2020.111483
OpenAlex ID: W4249873128
description: scientific article; zbMATH DE number 7345598