Curves of separatrix cycles of a quadratic system. The case of three antisaddles and one saddle
type: Item
instance of: scholarly article
title: Curves of separatrix cycles of a quadratic system. The case of three antisaddles and one saddle
zbMATH Open document ID: 1095.34529
DOI: 10.1023/A:1016049607087
author: S. I. Dovnar
author: Leonid Cherkas
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: Consider the differential system \[ \frac{dx}{dt}=-(1+x)y+\alpha Q(x,y),\quad \frac{dy}{dt}=x+\lambda y+ax^2+b(x+1)y+cy^2\equiv Q(x,y),\tag{*} \] where \(a,b, c,\alpha,\lambda\) are real parameters. The parameters \(\alpha,b,\lambda\) rotate the vector field (*). The authors prove that under some conditions there are exactly two values of the parameter \(\lambda\) such that (*) has a heteroclinic orbit with two saddles at infinity. The proof is based on the bifurcation theory and the theory of rotated vector fields.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1916042
zbMATH Keywords: rotated vector fields
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: a:1016049607087
OpenAlex ID: W172647015
description: scientific article; zbMATH DE number 1916042