Explosive route to chaos through a fractal torus in a generalized Lotka- Volterra model
type: Item
instance of: scholarly article
title: Explosive route to chaos through a fractal torus in a generalized Lotka- Volterra model
zbMATH Open document ID: 0668.92010
DOI: 10.1007/BF02458847
author: Nikola Samardzija
author: Larry D. Greller
published in: Bulletin of Mathematical Biology
publication date: 1988-01-01T00:00:00Z
review text: This paper is an informal treatment of the model \[ x'=x-xy+cx^ 2- azx^ 2,\quad y'=-x+xy,\quad z'=-bz+azx^ 2 \] where a,b,c\(\geq 0\). The authors call this a two-predator one -prey Lotka-Volterra system. Note that in the absence of predation prey grows to infinity. Stability of equilibria and bifurcations are discussed and computer simulations presented. The authors state that at \(b/a=1\) the system jumps into chaos through the birth of a fractal torus.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 4095270
zbMATH Keywords: three-dimensional system
zbMATH Keywords: non-transversal saddle connection type bifurcation
zbMATH Keywords: Hopf type bifurcation
zbMATH Keywords: two-predator one -prey Lotka-Volterra system
zbMATH Keywords: Stability of equilibria
zbMATH Keywords: bifurcations
zbMATH Keywords: computer simulations
zbMATH Keywords: chaos
zbMATH Keywords: fractal torus
reviewed by: M. Farkas
describes a project that uses: IMSL Numerical Libraries
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02458847
OpenAlex ID: W4245683389
description: scientific article; zbMATH DE number 4095270