Nonlinear Dynamics

, Volume 72, Issue 3, pp 499–505 | Cite as

Normal form of Bogdanov–Takens: styles and a hypernormalization method

  • Hamid Gazor


A brief review is stated on a hypernormalization method of autonomous differential equations in the vicinity of an equilibrium. The formalization is obtained from the method of cohomology spectral sequences. We skip the technical concepts such that it can be accessible for a broad audience. Three normal form styles are demonstrated by computing three different and known first-level normal forms of Bogdanov–Takens singularity.


Normal form Bogdanov–Takens singularity Spectral sequences method 



The author would like to acknowledge Majid Gazor’s useful discussions.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsMajlesi Branch, Islamic Azad UniversityIsfahanIran

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