Journal of Dynamical and Control Systems

, Volume 18, Issue 4, pp 529–549 | Cite as

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

  • Francisco A. Carrillo
  • Fernando Verduzco
  • Joaquín Delgado


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.

Key words and phrases

Takens-Bogdanov bifurcation Versal deformation Center manifold theory 

2000 Mathematics Subject Classification

53C17 22E30 49J15 


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Francisco A. Carrillo
    • 1
    • 2
  • Fernando Verduzco
    • 1
    • 2
  • Joaquín Delgado
    • 3
    • 4
  1. 1.HermosilloSonoraMexico
  2. 2.Departamento de MatemáticasUniversidad de SonoraSonoraMexico
  3. 3.Ciudad de Mexico D.F.SonoraMexico
  4. 4.Departamento de MatemáticasUAM-IztapalapaSonoraMexico

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