Stability for a competitive Lotka-Volterra system with delays
type: Item
instance of: scholarly article
title: Stability for a competitive Lotka-Volterra system with delays
zbMATH Open document ID: 1015.34060
DOI: 10.1016/S0362-546X(01)00881-1
author: Jin Zhen
author: Zhien Ma
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-11-28T00:00:00Z
review text: The authors consider the following Lotka-Volterra type competitive system with discrete delays \[ \dot x(t) =x(t)[b_1-a_{11}x(t-\tau_{11})-a_{12}y(t-\tau_{12})],\quad \dot y(t) =y(t)[b_2-a_{21}x(t-\tau_{21})-a_{22}y(t-\tau_{22})], \] with the initial conditions \[ \begin{aligned} x(t)&=\phi_1(t)\geq 0, \quad t\in[-\tau,0],\quad\phi_1(0)>0,\\ y(t)&=\phi_2(t)\geq 0,\quad t\in[-\tau,0],\quad\phi_2(0)>0,\\ \tau&=\max\{\tau_{ij}\},\end{aligned} \] where \(x(t), y(t)\) stand for densities of both the population at time \(t\), respectively, \(b_i, a_{ij}\) are all positive constants and \(\tau_{ij}\) are nonnegative. Conditions for local and global asymptotic stability of the positive equilibrium \(Z^*=(x^*,y^*)\) are obtained.
reviewed by: Alexander O. Ignatyev
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 1836635
zbMATH Keywords: delay differential equations
zbMATH Keywords: stability
MaRDI profile type: Publication
cites work: Convergence results in a well-known delayed predator-prey system
cites work: Discrete delay, distributed delay and stability switches
cites work: Stability Criteria for a System Involving Two Time Delays
cites work: Q4003237
cites work: Stability and delays in a predator-prey system
cites work: The Lyapunov Functionals for Delay Lotka--Volterra-Type Models
cites work: Delay differential equations: with applications in population dynamics
cites work: Permanence and global attractivity for competitive Lotka–Volterra systems with delay
cites work: Q3990387
cites work: Q4374087
cites work: Stability of predation models with time delay
description: scientific article; zbMATH DE number 1836635