Partial permanence and extinction in an N-species nonautonomous Lotka-Volterra competitive system
type: Item
instance of: scholarly article
title: Partial permanence and extinction in an N-species nonautonomous Lotka-Volterra competitive system
zbMATH Open document ID: 1188.34059
author: Jinxian Li
author: Jurang Yan
publication date: 2009-10-30T00:00:00Z
review text: The authors study the \(N\)-dimensional (N-species) differential system \[ u'_k(t)=u_k(t) \left[a_k(t)-\lambda g_k(t)-\sum_{l=1}^N b_{kl}(t) u_l(t) \right], \qquad 1\leq k\leq N, \] where \(a_k(t)\), \(b_{kl}(t)\), \(g_k(t)\) are bounded continuous functions on \([0,\infty)\) and \(b_{kl}(t)\geq 0\) for \(t\in[0,\infty)\), \(\lambda\geq 0\) is a constant. They show that certain average conditions involving the averages of the growth rates and the interaction coefficients imply the total persistence of all species. They also give computable conditions on the coefficients which imply the ultimate extinction of certain species.
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5623813
zbMATH Keywords: non-autonomous Lotka-Volterra system
zbMATH Keywords: competition
zbMATH Keywords: partial permanence
zbMATH Keywords: persistence
zbMATH Keywords: extinction
MaRDI profile type: Publication
full work available at URL: j.camwa.2007.03.018
OpenAlex ID: W2015362963
Wikidata QID: Q114672445
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DOI: 10.1016/J.CAMWA.2007.03.018
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 5623813