Bifurcation schemes of the Lorenz model
type: Item
instance of: scholarly article
title: Bifurcation schemes of the Lorenz model
zbMATH Open document ID: 0593.58025
DOI: 10.1016/0167-2789(84)90441-X
author: B. George
published in: Physica D
publication date: 1984-01-01T00:00:00Z
review text: The Lorenz equations have been investigated by many authors since Lorenz first suggested them as a model for fluid turbulence [J. Atmos. Sci. 20, 130 (1963)]. \textit{C. Sparrow} has published an exhaustive analysis of the dynamics of these equations [The Lorenz equations: bifurcations, chaos, and strange attractors (1982; Zbl 0504.58001)]. In this paper the authors make a global study of these equations which ties together many of the previously studied parameter regimes. In particular, the authors show that the transition to turbulent dynamics need not always occur as in some of the special cases that have been previously described. They present numerical evidence for the existence of tangent bifurcations at the endpoints of period-doubling sequences which do not give rise to intermittent turbulence.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 3953893
zbMATH Keywords: global study of the Lorenz equation
zbMATH Keywords: Lorenz equations
zbMATH Keywords: fluid turbulence
zbMATH Keywords: tangent bifurcations
zbMATH Keywords: intermittent turbulence
MaRDI profile type: Publication
cites work: Deterministic Nonperiodic Flow
cites work: Q4127550
cites work: Periodic Solutions and Bifurcation Structure at High R in the Lorenz Model
cites work: Q4158674
cites work: Preturbulence: A regime observed in a fluid flow model of Lorenz
cites work: Q4331516
cites work: Q3935898
cites work: A numerical approach to ergodic problem of dissipative dynamical systems.
cites work: Q3898227
cites work: Q4139853
cites work: Observation of a strange attractor
cites work: Q3869127
cites work: Q3879566
cites work: A description of the Lorenz attractor at high Prandtl number
cites work: The Lorenz equations: bifurcations, chaos, and strange attractors
cites work: The inverse scattering transform: Semi-infinite interval
full work available at URL: 0167-2789(84)90441-x
OpenAlex ID: W1990614122
description: scientific article; zbMATH DE number 3953893