Control of the n-dimensional Takens-Bogdanov bifurcation with applications

Francisco A. Carrillo*, Fernando Verduzco, Joaquín Delgado

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An n-dimensional nonlinear control system is considered, whose nominal vector field has a double-zero eigenvalue and no other eigenvalue on the imaginary axis, and then the idea is to find under which conditions there exists a scalar control law such that it is possible to establish a priori, that the closed loop system undergoes the controllable Takens-Bogdanov bifurcation. One application of this result is discussed.

Original languageEnglish
Pages (from-to)529-549
Number of pages21
JournalJournal of Dynamical and Control Systems
Issue number4
StatePublished - Oct 2012


  • Center manifold theory
  • Takens-Bogdanov bifurcation
  • Versal deformation


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