The discrete dynamics of symmetric competition in the plane
type: Item
instance of: scholarly article
title: The discrete dynamics of symmetric competition in the plane
zbMATH Open document ID: 0668.92011
DOI: 10.1007/BF00275495
author: Hong Jiang
author: Thomas D. Rogers
published in: Journal of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: This paper is a detailed study of the map \(F:R^ 2_+\mapsto R^ 2_+\) defined by \(F(x,y)=(f(x,y),\quad f(y,x))\) where \(f(x,y)=\exp (r- rx-sy),\) (r,s non-negative parameters). The iterates of this map represent the dynamics of competition between two species with discrete generation time. The map is symmetric: the intrinsic growth ``exponents'' r and the exponents representing the interspecific competition s are the same at the two species. Therefore the model is non-generic; nevertheless, its interesting and rich dynamics may help to understand what happens in such a situation. Fixed points, their stability, invariant attractive sets, period-two cycles, their stability, Hopf bifurcations from stable period-two cycles treated as fixed points of \(F^ 2\), and a possible cascade of period doubling bifurcations occur and are studied in an elegant exposition.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 39A99
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 4095271
zbMATH Keywords: discrete dynamical systems
zbMATH Keywords: competition
zbMATH Keywords: discrete generation time
zbMATH Keywords: Fixed points
zbMATH Keywords: stability
zbMATH Keywords: invariant attractive sets
zbMATH Keywords: period-two cycles
zbMATH Keywords: Hopf bifurcations
zbMATH Keywords: period doubling bifurcations
Wikidata QID: Q52614347
reviewed by: M. Farkas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4095271