The Tricomi problem for the Shimizu-Morioka dynamical system
type: Item
instance of: scholarly article
title: The Tricomi problem for the Shimizu-Morioka dynamical system
zbMATH Open document ID: 1269.34051
DOI: 10.1134/S1064562412060324
published in: Doklady Mathematics
publication date: 2013-04-03T00:00:00Z
review text: Consider the system \[ \begin{aligned} {dx\over dt} &= y,\\ {dy\over dt} &= x-ay- xz,\\ {dz\over dt} &= -bz+ x^2,\end{aligned}\tag{\(*\)} \] where \(a\) and \(b\) are real parameters. The author proves that, for a given \(b> 0\), there exists a number \(a(b)\geq 0\) such that \((*)\) has a homoclinic orbit to the origin. At the same time, the underlying scheme of the proof, the so-called Fisher principle, is justified.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6149510
zbMATH Keywords: Fisher principle
author: G. A. Leonov
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
cites work: Q3099080
cites work: On bifurcations of the Lorenz attractor in the Shimizu-Morioka model
full work available at URL: s1064562412060324
OpenAlex ID: W2057966489
description: scientific article; zbMATH DE number 6149510