Journal of Dynamical and Control Systems

, Volume 18, Issue 4, pp 529–549

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


    • Hermosillo
    • Departamento de MatemáticasUniversidad de Sonora
  • Fernando Verduzco
    • Hermosillo
    • Departamento de MatemáticasUniversidad de Sonora
  • Joaquín Delgado
    • Ciudad de Mexico D.F.
    • Departamento de MatemáticasUAM-Iztapalapa

DOI: 10.1007/s10883-012-9158-z

Cite this article as:
Carrillo, F.A., Verduzco, F. & Delgado, J. J Dyn Control Syst (2012) 18: 529. doi:10.1007/s10883-012-9158-z


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

Copyright information

© Springer Science+Business Media New York 2012