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International Journal of Mathematics and Mathematical Sciences
Volume 2016, Article ID 7658364, 12 pages
Research Article

On the Computation of Degenerate Hopf Bifurcations for -Dimensional Multiparameter Vector Fields

Department of Electrical & Computer Engineering, University of Patras, 26504 Patras, Greece

Received 18 December 2015; Revised 18 May 2016; Accepted 25 May 2016

Academic Editor: Harvinder S. Sidhu

Copyright © 2016 Michail P. Markakis and Panagiotis S. Douris. 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.


The restriction of an -dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.