Asymptotic behaviour of solutions of Lotka-Volterra systems
type: Item
instance of: scholarly article
title: Asymptotic behaviour of solutions of Lotka-Volterra systems
zbMATH Open document ID: 1113.34036
author: E. Wawiórko
author: J. S. Baris
author: P. J. Baris
published in: Nonlinear Analysis. Real World Applications
publication date: 2007-01-16T00:00:00Z
review text: Some new sufficient conditions are derived for the competitive exclusion of a few species of a Lotka-Volterra type system of the form \[ \dot x_k=x_k(\beta_{k1}(t)x_1+\dots+\beta_{kn}(t)x_n+\gamma_k(t)), \] where \(\beta_{kj}\) and \(\gamma_k\) are real-valued continuous functions on \(\mathbb R\), \(k,j=1,\dots,n\). The authors also give a proof of the extension of some results of their previous works and establish competitive exclusion of a few species in the system under conditions which are different from those of \textit{F. Montes de Oca} and \textit{M. L. Zeeman} [Math. Anal. Appl. 192, 360--370 (1995; Zbl 0830.34039)]. Conditions for the existence of finite escape times in solutions of the Lotka-Volterra systems and upper-bounds for these times are obtained. The approach is based on results of matrix Riccati equations.
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 32D10
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5116298
zbMATH Keywords: matrix Riccati equation
zbMATH Keywords: competitive exclusion principle
zbMATH Keywords: finite escape time
reviewed by: J. Michel Tchuenche
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2005.03.022
OpenAlex ID: W1986842978
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DOI: 10.1016/J.NONRWA.2005.03.022
description: scientific article; zbMATH DE number 5116298