Robust interval stability, persistence, and partial stability of Lotka-Volterra systems with time-delay
type: Item
instance of: scholarly article
title: Robust interval stability, persistence, and partial stability of Lotka-Volterra systems with time-delay
zbMATH Open document ID: 0857.34067
DOI: 10.1016/S0096-3003(96)90049-1
author: Jia Li
author: Xiaoxin Liao
published in: Applied Mathematics and Computation
publication date: 1997-03-06T00:00:00Z
review text: Consider the Lotka-Volterra system \[ x_i'(t)=x_i(t) \biggl(r_i+ \sum^n_{j=1} (a_{ij}x_j(t)+b_{ij} x_j(t-\tau_j)) \biggr),\qquad i=1,\dots,n \] with uncertain (interval) parameters \(\underline{a}_{ij}\leq a_{ij}\leq \overline{a}_{ij}\), etc. Suppose that there is a unique positive equilibrium \(x^*=(x^*_1,\dots,x^*_n)^\top\), \(x^*_i>0\). Conditions are given for \(x^*\) to be globally stable for any choice of the system parameters from the corresponding invervals. Also, conditions are derived for positiveness of the solutions satisfying \(x_i(0)>0\).
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 892435
zbMATH Keywords: Lotka-Volterra system
zbMATH Keywords: globally stable
zbMATH Keywords: positiveness of the solutions
reviewed by: Mihail M. Konstantinov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 892435