Journal of Dynamical and Control Systems

, Volume 18, Issue 4, pp 529-549

First online:

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

  • Francisco A. CarrilloAffiliated withHermosilloDepartamento de Matemáticas, Universidad de Sonora Email author 
  • , Fernando VerduzcoAffiliated withHermosilloDepartamento de Matemáticas, Universidad de Sonora
  • , Joaquín DelgadoAffiliated withCiudad de Mexico D.F.Departamento de Matemáticas, UAM-Iztapalapa

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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