COMPUTATION OF HOPF BRANCHES BIFURCATING FROM A HOPF/PITCHFORK POINT FOR PROBLEMS WITH Z_2-SYMMETRY

作     者：Bai－sheng Wu (Department of Mathematics,Jilin University, Changchun 130023, China)Tassilo Kupper (Institute of Mathematics, University of Cologne, D-50931 Koln, Germany) 

作者机构：吉林大学数学系 吉林 长春 Univeristy of Cologne 德国 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：1998年第16卷第5期

页      面：403-416页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Hopf/pitchfork point Z_2-symmetry Hopf point bifurcation Extended system 

摘      要：This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parametor nonlinear problem satisfying a Z2symnletry condition. Our aim is to present a new al,proach to the theoretical and computational analysis of the bifurcating Hopf branches at this singular point by using the system designed to calculate Hopf points and exploring its symmetry. It is shown that a Hopf/Pitchfork point is a pitchfork bifurcation point in the *** standard continuation and branch-switching can be used to compute these Hopf branches. In addition, an effect method based on the extended system of the singular points is developed for the computation of branch of secondary (nonsymmetric) Hopf points. The implementation of Newton s method for solving the extended system is also discussed. A numerical example is ***: Hopf/Pitchfork point, Z2-symmetry, Hopf point, bifurcation, Extended system