Hopf bifurcation in a delayed differential-algebraic biological economic system
type: Item
instance of: scholarly article
title: Hopf bifurcation in a delayed differential-algebraic biological economic system
zbMATH Open document ID: 1221.34227
author: Lulu Zhu
author: Boshan Chen
author: Guo-Dong Zhang
published in: Nonlinear Analysis. Real World Applications
publication date: 2011-05-02T00:00:00Z
review text: This paper deals with a predator-prey differential system incorporating harvesting effort on the prey and a constant time delay which represents the reaction time of the preys. The model is completed with an algebraic equation which incorporates the economic effect of harvesting, according to the economic theory proposed by Gordon in 1954. The main goal of the paper is to analyze the behaviour of the positive steady-state of this differential-algebraic system in terms of the delay considered as a varying parameter. Using the general theory of normal forms and the center manifold theory, the existence of a Hopf bifurcation is analyzed. The paper includes some numerical simulations to illustrate the analytical findings.
reviewed by: Eva Sánchez
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K21
Mathematics Subject Classification ID: 34K19
Mathematics Subject Classification ID: 34K17
zbMATH DE Number: 5882900
zbMATH Keywords: delayed differential-algebraic system
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: predator-prey economic system
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2010.11.003
OpenAlex ID: W2091878979
cites work: Chaos in a Lotka-Volterra predator-prey system with periodically impulsive ratio-harvesting the prey and time delays
cites work: Hopf bifurcation and stability analysis in a harvested one-predator-two-prey model
cites work: Optimal harvesting of diffusive models in a nonhomogeneous environment elena braverman, leonid braverman
cites work: Modelling and analysis of a prey-predator system with stage-structure and harvesting
cites work: The stability and Hopf bifurcation for a predator-prey system with time delay
cites work: Selective harvesting in a prey-predator fishery with time delay
cites work: Periodic Fox production harvesting models with delay
cites work: Local Hopf bifurcation and global periodic solutions in a delayed predator--prey system
cites work: Hopf bifurcation and stability of periodic solutions in a delayed eco-epidemiological system
cites work: Non-selective harvesting in prey--predator models with delay
cites work: Qualitative analysis of a predator-prey model with constant-rate prey harvesting incorporating a constant prey refuge
cites work: Bifurcations of a class of singular biological economic models
cites work: Hopf bifurcation and stability for a differential-algebraic biological economic system
cites work: Q4509338
cites work: Q3930015
cites work: Q4462600
cites work: Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
DOI: 10.1016/J.NONRWA.2010.11.003
description: scientific article; zbMATH DE number 5882900