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

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  • Michail P. Markakis
  • Panagiotis S. Douris

Abstract

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.

Suggested Citation

  • Michail P. Markakis & Panagiotis S. Douris, 2016. "On the Computation of Degenerate Hopf Bifurcations for -Dimensional Multiparameter Vector Fields," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2016, pages 1-12, June.
    • Handle: RePEc:hin:jijmms:7658364
    DOI: 10.1155/2016/7658364
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    References listed on IDEAS

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    1. Avila-Vales, Eric & Chan-Chí, Noé & García-Almeida, Gerardo E. & Vargas-De-León, Cruz, 2015. "Stability and Hopf bifurcation in a delayed viral infection model with mitosis transmission," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 293-312.
    2. Huang, Kuifei & Yang, Qigui, 2009. "Stability and Hopf bifurcation analysis of a new system," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 567-578.
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