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Volume 9, Issue 2
A Direct Method for Pitchfork Bifurcation Points

Zhong-Hua Yang

J. Comp. Math., 9 (1991), pp. 149-154.

Published online: 1991-09

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  • Abstract

To overcome the difficulty caused by the singularity at the pitchfork bifurcation points, we introduce the homotopy parameter so that the problem of computing the pitchfork bifurcation points can be transferred to that of computing the fold points of degree 3 with respect to the homotopy parameter. An extended system for pitchfork bifurcation points is given. The regularity of the extended system is proved. Finally, the numerical examples show the effectiveness of our method.

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@Article{JCM-9-149, author = {Yang , Zhong-Hua}, title = {A Direct Method for Pitchfork Bifurcation Points}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {2}, pages = {149--154}, abstract = {

To overcome the difficulty caused by the singularity at the pitchfork bifurcation points, we introduce the homotopy parameter so that the problem of computing the pitchfork bifurcation points can be transferred to that of computing the fold points of degree 3 with respect to the homotopy parameter. An extended system for pitchfork bifurcation points is given. The regularity of the extended system is proved. Finally, the numerical examples show the effectiveness of our method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9387.html} }
TY - JOUR T1 - A Direct Method for Pitchfork Bifurcation Points AU - Yang , Zhong-Hua JO - Journal of Computational Mathematics VL - 2 SP - 149 EP - 154 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9387.html KW - AB -

To overcome the difficulty caused by the singularity at the pitchfork bifurcation points, we introduce the homotopy parameter so that the problem of computing the pitchfork bifurcation points can be transferred to that of computing the fold points of degree 3 with respect to the homotopy parameter. An extended system for pitchfork bifurcation points is given. The regularity of the extended system is proved. Finally, the numerical examples show the effectiveness of our method.

Yang , Zhong-Hua. (1991). A Direct Method for Pitchfork Bifurcation Points. Journal of Computational Mathematics. 9 (2). 149-154. doi:
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