A predator-prey Gompertz model with time delay and impulsive perturbations on the prey
type: Item
instance of: scholarly article
title: A predator-prey Gompertz model with time delay and impulsive perturbations on the prey
zbMATH Open document ID: 1200.34101
DOI: 10.1155/2009/256195
author: Jianwen Jia
author: Chunhua Li
published in: Discrete Dynamics in Nature and Society
publication date: 2010-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/223644
review text: The authors study existence of a periodic solution, permanence and global stability for the following impulsive system \[ \begin{cases} \frac{dx}{dt}=rx(t)\ln \frac{K}{x(t)}-\frac{x^2(t)}{1+mx^2(t)}y(t), \\ \frac{dy}{dt}=\beta \frac{x^2(t-\tau)}{1+mx^2(t-\tau)}y(t-\tau)-dy(t),& t\not =nT,\;n\in N, \\ \Delta x(t)=-px(t),~\Delta y(t)=0,& t=nt,\;n\in N. \end{cases} \]
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 5701459
zbMATH Keywords: predator-prey Gomperrtz model
zbMATH Keywords: time delay
zbMATH Keywords: impulsive perturmations
zbMATH Keywords: global stability
zbMATH Keywords: permanence
reviewed by: Leonid Berezansky
MaRDI profile type: Publication
OpenAlex ID: W1989485540
Wikidata QID: Q58647433
cites work: The periodic predator-prey Lotka-Volterra model
cites work: Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations
cites work: Q4325523
cites work: Chaos in three species food chain system with impulsive perturbations
cites work: Boundedness for impulsive delay differential equations and applications to population growth models.
cites work: A stage-structured Holling mass defence predator-prey model with impulsive perturbations on predators
cites work: Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination
cites work: Q3995625
cites work: ANALYSIS OF STABILITY AND PERSISTENCE IN A RATIO-DEPENDENT PREDATOR-PREY RESOURCE MODEL
Recommended article: A new stage structured predator-prey Gompertz model with time delay and impulsive perturbations on the prey
Recommended article: A stage-structured predator-prey model with time delay and impulsive effects
Recommended article: Q3538391
Recommended article: Q3054493
Recommended article: Q3640366
Recommended article: Q3640139
Recommended article: Q2951529
Recommended article: Q5296987
Recommended article: The dynamics of an impulsive delay predator-prey model with variable coefficients
Recommended article: Q3110234
description: scientific article; zbMATH DE number 5701459