Competing species model with behavioral adaptation
type: Item
instance of: scholarly article
title: Competing species model with behavioral adaptation
zbMATH Open document ID: 0611.92024
DOI: 10.1007/BF00275683
author: V. W. Noonburg
published in: Journal of Mathematical Biology
publication date: 1986-01-01T00:00:00Z
review text: As said in the abstract, the author ''studies the properties of a modified Lotka-Volterra model for two competing species, in which the coefficients of the interaction terms are time-dependent averages of the level of interaction over the entire past.'' The main analytical effect of this seems to be an increased nonlinearity which is reflected by the existence of up to 6 stationary states in a certain range of the parameters. A noticeable fact is that none of the 3 permanent equilibria corresponding to partial or total extinction is stable. This is in contrast to the usual model. The other correspond to coexistence of both species, with a dominant one. The author concentrates on the case of three interior equilibria, of which one (intermediate) is always unstable and the other two (extreme) are separately stable or unstable depending on interaction parameters. Moreover, the author was able to find numerically a nonempty region of these parametes where no equilibrium is stable and numerical simulation suggests the existence of solutions passing successively near each of the extreme equilibria, and possibly of a limit cycle. We may observe finally that functionally the equation belongs to the class of infinite delay differential systems. But, treating as an independent variable each term bearing the dependence on the past, it can be reduced to a system of 4 ordinary differential equations, as the author does. This remark also aims at indicating that the study performed in this paper is far from being trivial.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 3989164
zbMATH Keywords: critical points
zbMATH Keywords: behavioral adaptation
zbMATH Keywords: oscillatory solutions
zbMATH Keywords: modified Lotka-Volterra model
zbMATH Keywords: competing species
zbMATH Keywords: coexistence
zbMATH Keywords: interior equilibria
zbMATH Keywords: limit cycle
zbMATH Keywords: infinite delay differential systems
Wikidata QID: Q52650822
reviewed by: Ovide Arino
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00275683
OpenAlex ID: W2041860223
description: scientific article; zbMATH DE number 3989164