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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 420897, 9 pages
http://dx.doi.org/10.1155/2013/420897
Research Article

Codimension-m Bifurcation Theorems Applicable to the Numerical Verification Methods

Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

Received 20 December 2012; Revised 13 April 2013; Accepted 18 April 2013

Academic Editor: William J. Layton

Copyright © 2013 Tadashi Kawanago. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish codimension-m bifurcation theorems applicable to the numerical verification methods. They are generalization of codimension-1 bifurcation theorems established by (Kawanago, 2004). As a numerical example, we treat Hopf bifurcation, which is codimension-2 bifurcation.