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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2016/7658364 |
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| _version_ | 1832551102274338816 |
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| author | Michail P. Markakis Panagiotis S. Douris |
| author_facet | Michail P. Markakis Panagiotis S. Douris |
| author_sort | Michail P. Markakis |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3531cb1e464740f3999fba333d70699e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3531cb1e464740f3999fba333d70699e2025-02-03T06:04:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252016-01-01201610.1155/2016/76583647658364On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector FieldsMichail P. Markakis0Panagiotis S. Douris1Department of Electrical & Computer Engineering, University of Patras, 26504 Patras, GreeceDepartment of Electrical & Computer Engineering, University of Patras, 26504 Patras, GreeceThe 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.http://dx.doi.org/10.1155/2016/7658364 |
| spellingShingle | Michail P. Markakis Panagiotis S. Douris On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields International Journal of Mathematics and Mathematical Sciences |
| title | On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields |
| title_full | On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields |
| title_fullStr | On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields |
| title_full_unstemmed | On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields |
| title_short | On the Computation of Degenerate Hopf Bifurcations for n-Dimensional Multiparameter Vector Fields |
| title_sort | on the computation of degenerate hopf bifurcations for n dimensional multiparameter vector fields |
| url | http://dx.doi.org/10.1155/2016/7658364 |
| work_keys_str_mv | AT michailpmarkakis onthecomputationofdegeneratehopfbifurcationsforndimensionalmultiparametervectorfields AT panagiotissdouris onthecomputationofdegeneratehopfbifurcationsforndimensionalmultiparametervectorfields |