Weak centers and bifurcation of critical periods in reversible cubic systems
type: Item
instance of: scholarly article
title: Weak centers and bifurcation of critical periods in reversible cubic systems
zbMATH Open document ID: 0962.34025
DOI: 10.1016/S0898-1221(00)00195-4
author: Xiaorong Hou
author: Zhenbing Zeng
author: Weinian Zhang
publication date: 2001-01-14T00:00:00Z
review text: This paper is concerned with planar reversible cubic differential systems with a center. An inductive algorithm to compute the period coefficients is developed. Using a computer algebra program, the algorithm is applied to study the order of the period function at the origin. The following systems are studied in more detail, \[ \dot x= -y- ax^2+ ay^2+ a_3 x^2 y+ a_4 y^3,\quad \dot y= x- 2axy+ b_2 x^3+ b_3 xy^2. \] In their main result, the authors prove that, for \(j= 1,\dots, 4\), there exists such a system having \(j\) critical periods.
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1550635
zbMATH Keywords: bifurcation
zbMATH Keywords: planar reversible cubic differential systems
zbMATH Keywords: center
zbMATH Keywords: critical periods
reviewed by: Marco Sabatini
MaRDI profile type: Publication
cites work: Q4004269
cites work: A class of cubic differential systems with 6-tuple focus
cites work: A Cubic System with Eight Small-Amplitude Limit Cycles
cites work: Q3948194
cites work: Bifurcation of Critical Periods for Plane Vector Fields
cites work: Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree
cites work: Associative differential operations
cites work: Q3737533
cites work: Q4293510
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1550635