- Journal Home
- Volume 42 - 2024
- Volume 41 - 2023
- Volume 40 - 2022
- Volume 39 - 2021
- Volume 38 - 2020
- Volume 37 - 2019
- Volume 36 - 2018
- Volume 35 - 2017
- Volume 34 - 2016
- Volume 33 - 2015
- Volume 32 - 2014
- Volume 31 - 2013
- Volume 30 - 2012
- Volume 29 - 2011
- Volume 28 - 2010
- Volume 27 - 2009
- Volume 26 - 2008
- Volume 25 - 2007
- Volume 24 - 2006
- Volume 23 - 2005
- Volume 22 - 2004
- Volume 21 - 2003
- Volume 20 - 2002
- Volume 19 - 2001
- Volume 18 - 2000
- Volume 17 - 1999
- Volume 16 - 1998
- Volume 15 - 1997
- Volume 14 - 1996
- Volume 13 - 1995
- Volume 12 - 1994
- Volume 11 - 1993
- Volume 10 - 1992
- Volume 9 - 1991
- Volume 8 - 1990
- Volume 7 - 1989
- Volume 6 - 1988
- Volume 5 - 1987
- Volume 4 - 1986
- Volume 3 - 1985
- Volume 2 - 1984
- Volume 1 - 1983
Cited by
- BibTex
- RIS
- TXT
This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parameter nonlinear problem satisfying a $Z_2$-symmetry condition. Our aim is to present a new approach 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 system. Hence 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 (non-symmetric) Hopf points. The implementation of Newton's method for solving the extended system is also discussed. A numerical example is given.
}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9171.html} }This paper is concerned with the computation of Hopf branches emanating from a Hopf/Pitchfork point in a two-parameter nonlinear problem satisfying a $Z_2$-symmetry condition. Our aim is to present a new approach 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 system. Hence 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 (non-symmetric) Hopf points. The implementation of Newton's method for solving the extended system is also discussed. A numerical example is given.