Stable periodic solution of a discrete periodic Lotka-Volterra competition system
type: Item
instance of: scholarly article
title: Stable periodic solution of a discrete periodic Lotka-Volterra competition system
zbMATH Open document ID: 1019.39004
DOI: 10.1016/S0022-247X(02)00611-X
author: Zhan Zhou
author: Yuming Chen
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-04-09T00:00:00Z
review text: Consider the following discrete Lotka-Volterra competition system \[ \begin{cases} x(n+1)= x(n)\exp \biggl[r_1(n) \bigl(1-x(n)/K_1(n)-\mu_2(n) y(n) \bigr) \biggr],\\ y(n+1)=y(n) \exp\biggl[r_2(n) \bigl(1-\mu_1(n)x(n)-y(n) /K_2 (n)\bigr) \biggr] \end{cases} \] where \(K_i(n)\), \(r_i(n)\) and \(\mu_i(n)\), \(i=1,2\) are bounded non-negative sequences. Sufficient conditions are given for the persistence of the system, i.e. the existence of a compact subset \(E\subset \mathbb{R}^2_+\) such that each solution will eventually enter and remain in \(E\). The existence and stability of periodic solution is established, too.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 1895773
zbMATH Keywords: Lotka-Volterra competition system
zbMATH Keywords: persistence
zbMATH Keywords: periodic solution
zbMATH Keywords: global stability
reviewed by: Dobiesław Bobrowski
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00611-x
OpenAlex ID: W1967765737
description: scientific article; zbMATH DE number 1895773