Generalized Lorenz-type systems
type: Item
instance of: scholarly article
title: Generalized Lorenz-type systems
zbMATH Open document ID: 0857.34001
author: Mostafa A. Abdelkader
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-03-17T00:00:00Z
review text: The author studies generalization of the Lorenz system of the form \(x'=a(y-x)\), \(y'=f(x)- ny-xz\), \(z'=xy-bz\). He first shows that for the classical choice \(f(x)=rx\) and some special choices of parameters and initial values the exact solutions of the Lorenz system may be obtained in terms of Jacobian elliptic functions. Then he shows that for a few choices of \(f\), in particular \(f(x)= rx+x^3/(2a)\) it is possible to obtain exact formulas for all solutions of the considered system in terms of Bessel functions or modified Bessel functions. Moreover, for some parameter values these solutions exhibit chaotic behavior.
reviewed by: Marian Mrozek
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 33C10
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 902522
zbMATH Keywords: generalization of the Lorenz system
zbMATH Keywords: exact solutions
zbMATH Keywords: Jacobian elliptic functions
zbMATH Keywords: modified Bessel functions
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0123
OpenAlex ID: W2022857059
DOI: 10.1006/JMAA.1996.0123
description: scientific article; zbMATH DE number 902522