Poincaré bifurcations in polynomial differential systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 0979.34034
author: Dingjun Luo
publication date: 2001-07-11T00:00:00Z
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1616914
zbMATH Keywords: limit cycle
zbMATH Keywords: Poincaré bifurcation
zbMATH Keywords: Hopf bifurcation
MaRDI profile type: Publication
title: Poincaré bifurcations in polynomial differential systems
published in: Systems Science and Mathematical Sciences
review text: The author considers Poincaré bifurcations for polynomial differential systems. Usually Pontryagin's method of perturbed Hamiltonian systems is used to deal with such problems by studying the number and multiplicity of zeros for certain Abelian integrals. Many results have been given for concrete polynomial systems applying this method. NEWLINENEWLINENEWLINEHowever, since the method is inapplicable to the case where the perturbed system has a complicated Hamiltonian function or the system is integrable but non-Hamiltonian, the author suggests another approach to avoid complicated calculations of the Abelian integrals. He studies the Poincaré bifurcation starting from the Hopf bifurcations of all possible orders and gives a complete result for the Poincaré bifurcations in quadratic systems of Bautin's form.
reviewed by: Valery A. Gaiko
description: scientific article; zbMATH DE number 1616914