The diffusionless Lorenz equations; Shil'nikov bifurcations and reduction to an explicit map
type: Item
instance of: scholarly article
title: The diffusionless Lorenz equations; Shil'nikov bifurcations and reduction to an explicit map
zbMATH Open document ID: 0956.37038
DOI: 10.1016/S0167-2789(00)00033-6
author: Gerard van der Schrier
author: Leo R. M. Maas
published in: Physica D
publication date: 2000-10-08T00:00:00Z
review text: The authors investigate an energetically closed model for convection, a version of the classical Lorenz model, in the limit for high Prandtl and Rayleigh numbers, i.e. diffusionless convection. They find an exact solution to this model, serving as a strong forcing limit, being a new integrable case of Lorenz equations. The bifurcations are studied mainly via a further reduction to an explicit analytic map and numerical exploration, which show that these essentially involve Shil'nivkov-type homoclinic bifurcations with a self similar behaviour in the parameter.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 34C99
zbMATH DE Number: 1514728
zbMATH Keywords: diffusionless Lorenz equations
zbMATH Keywords: Shilnikov homoclinic bifurcations
zbMATH Keywords: reduction to map
reviewed by: Jens D. M. Rademacher
describes a project that uses: AUTO
describes a project that uses: AUTO-86
MaRDI profile type: Publication
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full work available at URL: s0167-2789(00)00033-6
OpenAlex ID: W2171018278
Wikidata QID: Q127983056
description: scientific article; zbMATH DE number 1514728