On the cyclicity of a 2-polycycle for quadratic systems
type: Item
instance of: scholarly article
title: On the cyclicity of a 2-polycycle for quadratic systems
zbMATH Open document ID: 1081.34512
author: Cheng Yang
author: Maoan Han
published in: Chaos, Solitons and Fractals
publication date: 2005-04-18T00:00:00Z
review text: Consider a quadratic system in the plane of the form \[ x'=H_y+\varepsilon P(x,y),\quad y'=-H_x+\varepsilon Q(x,y), \] where \(\epsilon\) is a small parameter and \(H\) is cubic in \((x,y)\). It is assumed that for \(\varepsilon=0\), the system has a heteroclinic loop \(L\) with two hyperbolic saddles belonging to \(\{H=0\}\). The authors give conditions under which the loop \(L\) generates at most two limit cycles (or no cycles) for small \(\varepsilon\).
reviewed by: Sergei Yu. Pilyugin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 2158598
MaRDI profile type: Publication
full work available at URL: j.chaos.2004.07.008
OpenAlex ID: W2019178746
cites work: Persistence of invariant tori in generalized Hamiltonian systems
cites work: Elementary graphics of cyclicity 1 and 2
cites work: Cyclicity of planar homoclinic loops and quadratic integrable systems
cites work: Cyclicity of homoclinic loops and degenerate cubic Hamiltonians
cites work: Cyclicity 1 and 2 conditions for a 2-polycycle of integrable systems on the plane
cites work: On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems
cites work: Higher-order Melnikov functions for degenerate cubic Hamiltonians
cites work: Generalized Hopf Bifurcation and Its Dual Generalized Homoclinic Bifurcation
cites work: HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
cites work: On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
cites work: Q3715459
DOI: 10.1016/J.CHAOS.2004.07.008
description: scientific article; zbMATH DE number 2158598