Attractors of convex maps with positive Schwarzian derivative in the presence of noise
type: Item
instance of: scholarly article
title: Attractors of convex maps with positive Schwarzian derivative in the presence of noise
zbMATH Open document ID: 0602.58026
DOI: 10.1016/0167-2789(84)90182-9
author: Gottfried Mayer-Kress
author: H. Haken
published in: Physica D
publication date: 1984-01-01T00:00:00Z
review text: A two-parameter family of the functions \[ f_{r,b}(x)=a_{r,b}x(1- x)(1+bx(1-3x+2(2-x)x^ 2)) \] where \(a_{r,b}=4r/(1+b/8)\) and \(x\in [0,1]\), is studied numerically. The \(f_{r,0}\) is the known logistic system. The authors obtain, by varying parameter b, two coexisting attractors. The role of positive Schwarzian derivative is discussed and the influence of noise on these bifurcation phenomena is mentioned as well.
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 3971820
zbMATH Keywords: strange attractor
zbMATH Keywords: noise
zbMATH Keywords: logistic system
zbMATH Keywords: Schwarzian derivative
reviewed by: A. Klíč
MaRDI profile type: Publication
full work available at URL: 0167-2789(84)90182-9
OpenAlex ID: W2069755905
cites work: On the abundance of aperiodic behaviour for maps on the interval
cites work: Roads to turbulence in dissipative dynamical systems
cites work: Universal properties of maps on an interval
cites work: Note concerning our paper ''On the nature of turbulence''. Commun. math. Phys. 20, 167-192 (1971)
cites work: Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
cites work: Stable Orbits and Bifurcation of Maps of the Interval
cites work: The influence of noise on the logistic model
cites work: Q3319982
cites work: A two-dimensional mapping with a strange attractor
cites work: On the abnormality of period doubling bifurcations: in connection with the bifurcation structure in the Belousov-Zhabotinsky reaction system.
cites work: Q3733844
cites work: Symbolic dynamics of one-dimensional maps: Entropies, finite precision, and noise
cites work: Computing the topological entropy of maps
cites work: Preturbulence: A regime observed in a fluid flow model of Lorenz
cites work: Intermittency in the presence of noise
cites work: Small random perturbations of dynamical systems and the definition of attractors
description: scientific article; zbMATH DE number 3971820