On a model of competition in periodic environments
type: Item
instance of: scholarly article
title: On a model of competition in periodic environments
zbMATH Open document ID: 0872.39009
DOI: 10.1016/S0096-3003(96)00044-6
author: Pingzhou Liu
author: K. Gopalsamy
published in: Applied Mathematics and Computation
publication date: 1997-05-05T00:00:00Z
review text: The authors study the following discrete-time analogue of the Lotka-Volterra competition model: \[ x_i(n+1)= b_i(n)x_i(n)\Biggl/ \Biggl[1+ \sum_{j=1}^m c_{ij}(n)x_j(n)\Biggr], \qquad i=1,\dots, m;\quad n\in\mathbb{N}, \] where \(\{b_i(n)\}\), \(\{c_{ij}(n)\}\) are positive periodic sequences with a common period. The sufficient conditions for the existence and global attractivity of a positive periodic solution are given. Asymptotic bounds for arbitrary positive solutions of the system in terms of related periodic solutions are also presented.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 93C55
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1006496
zbMATH Keywords: discrete-time Lotka-Volterra competition model
zbMATH Keywords: asymptotic bounds
zbMATH Keywords: global attractivity
zbMATH Keywords: positive periodic solution
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1006496