Non-selective harvesting in prey--predator models with delay
type: Item
instance of: scholarly article
title: Non-selective harvesting in prey--predator models with delay
zbMATH Open document ID: 1112.34057
author: U. K. Pahari
author: T. K. Kar
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2006-10-31T00:00:00Z
review text: The authors study the following two delayed prey-predator models with nonselective harvesting: \[ \begin{aligned} \frac{dx}{dt} & = xg(x(t-\tau))-yp(x)-q_1E_1x, \\ \frac{dy}{dt} & = y[-d+\alpha p(x)]-q_2E_2y, \end{aligned} \] and \[ \begin{aligned} \frac{dx}{dt} & = xg(x)-yp(x)-q_1E_1x, \\ \frac{dy}{dt} & = y[-d+\alpha p(x(t-\tau))]-q_2E_2y. \end{aligned} \] Sufficient conditions for the stability of the only interior equilibrium are established. When this equilibrium loses stability, Hopf bifurcation will occur. These results indicate that the time delay may cause a stable equilibrium to become unstable and even a switching of stability, on the other hand, harvesting effort has a stabilizing effect on the equilibrium if it is under the critical harvesting effort level.
reviewed by: Yuming Chen
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K18
zbMATH DE Number: 5069041
zbMATH Keywords: prey-predator
zbMATH Keywords: nonselective harvesting
zbMATH Keywords: delay
zbMATH Keywords: equilibrium
zbMATH Keywords: stability
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: limit cycle
Wikidata QID: Q115578446
MaRDI profile type: Publication
full work available at URL: j.cnsns.2004.12.011
OpenAlex ID: W2045002267
cites work: Q3997210
cites work: Stability regions and transition phenomena for harvested predator-prey systems
cites work: Stability regions in predator-prey systems with constant-rate prey harvesting
cites work: Coexistence Region and Global Dynamics of a Harvested Predator-Prey System
cites work: An analysis of an ordinary differential equation model for a two-species predator-prey system with harvesting and stocking
cites work: Q4225223
cites work: A predator prey model with age structure
cites work: Delay differential equations: with applications in population dynamics
cites work: Q4003237
cites work: Delays in recruitment at different trophic levels: Effects on stability
cites work: Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays
cites work: Convergence results in a well-known delayed predator-prey system
cites work: Selective harvesting in a prey-predator fishery with time delay
cites work: Uniqueness of limit cycles in Gause-type models of predator-prey systems
DOI: 10.1016/J.CNSNS.2004.12.011
Recommended article: On a predator prey model with nonlinear harvesting and distributed delay
Recommended article: Predator-prey models with delay and prey harvesting
Recommended article: Dynamic behaviour of a delayed predator-prey model with harvesting
Recommended article: Q3110234
Recommended article: Selective harvesting in a prey-predator fishery with time delay
Recommended article: On a diffusive predator-prey model with nonlinear harvesting
Recommended article: Q3569613
Recommended article: A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH DELAY AND HARVESTING
Recommended article: Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting
Recommended article: DYNAMICAL BEHAVIOR OF A HARVESTED PREY-PREDATOR MODEL WITH STAGE STRUCTURE AND DISCRETE TIME DELAY
description: scientific article; zbMATH DE number 5069041