Global attractivity in delay ``food-limited'' models with exponential impulses.
type: Item
instance of: scholarly article
title: Global attractivity in delay ``food-limited'' models with exponential impulses.
zbMATH Open document ID: 1047.34086
DOI: 10.1016/S0022-247X(03)00543-2
author: Yuji Liu
author: Weigao Ge
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-11-19T00:00:00Z
review text: The authors obtain several sufficient conditions for the global attractivity of the positive equilibrium of the following impulsive system \[ \begin{aligned} N'(t)&= p(t)N(t)\frac{1-N(t-\tau)}{1+\lambda N(t-\tau)},\quad t\geq 0,\;t\neq t_k,\\ N(t_k^{+})&= N(t_k)^{1+b_k},\quad N(t)=\varphi(t),\quad t\in[-\tau,0], \end{aligned} \] with \(p(t)>0,~\lambda>0,~\tau>0,~b_k>-1.\) In particular, they prove the following theorem: Suppose that for any \(\varepsilon>0\) there exists an integer \(N\) such that \[ \prod_{k=n}^{n+m}(1+b_k)<1+\varepsilon,\quad \text{for}\quad n>N,\;m\geq 0. \] If, in addition, \[ \int_0^{\infty} p(s)\prod_{0\leq t_k<s}(1+b_k)^{-1}\,ds =+\infty, \] \[ \limsup_{t\rightarrow\infty} \int_{t-\tau}^t p(s)\prod_{t-\tau\leq t_k<s} (1+b_k)^{-1}ds\leq \tfrac{3}{2}(1+\lambda), \] then every positive solution of (1) tends to the equilibrium \(N\equiv1\) as \(t\) tends to infinity.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K45
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2006019
zbMATH Keywords: food-limited delay population model
zbMATH Keywords: global attractivity
zbMATH Keywords: impulses
reviewed by: Leonid Berezansky
MaRDI profile type: Publication
cites work: Time lags in a “food–limited” population
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full work available at URL: s0022-247x(03)00543-2
OpenAlex ID: W1975152416
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description: scientific article; zbMATH DE number 2006019