Conditions for the origin to be a center and the bifurcation of limit cycles in a class of cubic systems
type: Item
instance of: scholarly article
title: Conditions for the origin to be a center and the bifurcation of limit cycles in a class of cubic systems
zbMATH Open document ID: 0887.34024
DOI: 10.1007/BF02882836
author: Jiehua Zhu
author: Siming Zhu
published in: Chinese Science Bulletin
publication date: 1998-05-14T00:00:00Z
review text: This paper considers the following cubic system of center and focus type \[ \begin{aligned} \dot x & =y+ax^iy^j =X(x,y) \\ \dot y & =- x+bx^2 +cy^2 +dx^3 +exy^2= Y(x,y) \end{aligned} \] in different cases of \(i\) and \(j\), where \(i+j=2,3\). The authors use the classical method of Lyapunov and calculate focal values using the computer to decide the conditions for the origin to be a center and the order of the origin as a finite focus.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 1091412
zbMATH Keywords: limit cycle
zbMATH Keywords: cubic system
zbMATH Keywords: center
zbMATH Keywords: focus
reviewed by: Lansun Chen
MaRDI profile type: Publication
cites work: Q3700869
cites work: Q5844069
description: scientific article; zbMATH DE number 1091412