Perfect harmony: The discrete dynamics of cooperation
type: Item
instance of: scholarly article
title: Perfect harmony: The discrete dynamics of cooperation
zbMATH Open document ID: 0729.92022
DOI: 10.1007/BF00178325
published in: Journal of Mathematical Biology
publication date: 1990-01-01T00:00:00Z
review text: The paper studies the dynamical system \[ x_{n+1}=x_ n\exp (r(1-x_ n)+sy_ n),\quad y_{n+1}=y_ n\exp (r(1-y_ n)+sx_ n),\quad n=0,1,2,... \] with positive \(r,s,x_ 0,y_ 0\), and in particular its stretching and folding actions and its Hopf bifurcations. Also an approximating version with truncated Taylor series for both \(e^{sy_ n}\) and \(e^{sx_ n}\) is studied. The paper ends with a report on extensive computer simulations, including a bifurcation diagram describing the evolution from a stable attracting circle to a presumed strange attractor.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 4207830
zbMATH Keywords: dynamics of cooperation
zbMATH Keywords: discrete dynamical systems
zbMATH Keywords: Lotka-Volterra cooperation
zbMATH Keywords: permanence
zbMATH Keywords: stretching
zbMATH Keywords: folding
zbMATH Keywords: Hopf bifurcations
zbMATH Keywords: truncated Taylor series
zbMATH Keywords: computer simulations
zbMATH Keywords: stable attracting circle
zbMATH Keywords: strange attractor
Wikidata QID: Q113910002
author: Wieslaw Krawcewicz
author: Thomas D. Rogers
reviewed by: Lothar Berg
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00178325
OpenAlex ID: W2008691667
description: scientific article; zbMATH DE number 4207830