Harmless delays for permanence and impersistence of a Lotka-Volterra discrete predator-prey system
type: Item
instance of: scholarly article
title: Harmless delays for permanence and impersistence of a Lotka-Volterra discrete predator-prey system
zbMATH Open document ID: 1005.39013
DOI: 10.1016/S0362-546X(01)00778-7
author: Yasuhisa Saito
author: T. Hara
author: Wanbiao Ma
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: The main result is the following Theorem 1: If the inequalities \[ r_1\sum^m_{j=1} b_{2j}-r_2 \sum^m_{j=1} b_{1j}>0,\;r_1\sum^m_{j =1} a_{2j}+r_2 \sum^m_{j=1} a_{1j}>0 \] hold, then the Lotka-Volterra discrete predator-prey system \[ \begin{gathered} x(n+1)= x(n)\exp \left[r_1-\sum^m_{j=1} a_{1j}x (n-k_{ij}) -\sum^m_{j=1} b_{1j}y (n-k_{2j})\right],\\ y(n+1)= y(n)\exp \left[r_2 +\sum^m_{j=1} a_{2j}x(n-l_{1j}) -\sum^m_{j=1} b_{2j} y(n-l_{2j}) \right],\end{gathered} \] is permanent for nonnegative integers \(k_{ij}\) and \(l_{ij}\) \((i=1, 2,j=1,\dots,m)\). Here \(r_1\) and \(r_2\) are constants and \(a_{ij}\) and \(b_{ij}\) are nonnegative constants. The existence of an equilibrium and the impersistence of the system are considered too.
reviewed by: Dobiesław Bobrowski
Mathematics Subject Classification ID: 39A11
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39B05
zbMATH DE Number: 1788036
zbMATH Keywords: system with delays
zbMATH Keywords: permanent system
zbMATH Keywords: impersistent system
zbMATH Keywords: Lotka-Volterra discrete predator-prey system
Wikidata QID: Q115564253
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00778-7
OpenAlex ID: W2088935924
description: scientific article; zbMATH DE number 1788036