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

The restriction of an n-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 calcul...

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Bibliographic Details
Main Authors: Michail P. Markakis, Panagiotis S. Douris
Format: Article
Language:English
Published: Wiley 2016-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2016/7658364
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Summary:The restriction of an n-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.
ISSN:0161-1712
1687-0425