Global dynamics of the periodic logistic system with periodic impulsive perturbations.
type: Item
instance of: scholarly article
title: Global dynamics of the periodic logistic system with periodic impulsive perturbations.
zbMATH Open document ID: 1054.34015
author: Xianning Liu
author: Lansun Chen
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-01-26T00:00:00Z
review text: The authors consider the impulsive differential logistic equation \[ x'(t)= x(t)\bigl(r(t) -a(t)x(t)\bigr), \quad t\neq t_k,\;k\in \mathbb N,\tag{1} \] \[ \Delta x(t_k)= b_k x(t_k),\;k\in \mathbb N,\tag{2} \] where \(t_0=0<t_1< \cdots < t_k<t_{k+1}<\dots\), \(\Delta x(t_k)=x(t^+_k)-x(t_k)\), the functions \(r\) and \(a\) are piecewise continuous with a discontinuity of first kind \(t_k\), \(k=0,1,\dots\). (1) is \(\omega\)-periodic, i.e., \(r(t+\omega)= r(t)\), \(a(t+\omega)= a(t)\), \(t\in\mathbb R\) and (2) is \(T\)-periodic. Sufficient conditions for the existence of solutions of (1), (2), are derived taking into account whether \(\gamma=\frac{\omega}{T}\) is a rational or irrational number.
reviewed by: S. Kostadinov
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 2032970
zbMATH Keywords: Impulsive perturbation
zbMATH Keywords: Logistic system
zbMATH Keywords: Global asymptotic stability
zbMATH Keywords: Extinction
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.09.058
OpenAlex ID: W2040651653
cites work: Periodic Time-Dependent Predator-Prey Systems
cites work: Q4139908
cites work: Q3901357
cites work: Optimal harvesting policy for single population with periodic coefficients
cites work: Perturbation theorems for systems with impulse effect
cites work: Q3995625
cites work: Q4280625
cites work: Permanence of population growth models with impulsive effects
cites work: Impulsive control of a Lotka-Volterra system
cites work: A mathematical model of periodically pulsed chemotherapy: Tumor recurrence and metastasis in a competitive environment
cites work: Q4487445
cites work: The periodic predator-prey Lotka-Volterra model
cites work: Q4003604
cites work: Q3995227
cites work: Practical bifurcation and stability analysis: from equilibrium to chaos.
DOI: 10.1016/J.JMAA.2003.09.058
description: scientific article; zbMATH DE number 2032970