Computation of Normal Forms of Bogdanov-Takens Singularities for High Dimensional Nonlinear Systems
Abstract
A new computation of the normal forms of Bogdanov-Takens singularities is developed in this paper. In the theoretical model for the nonplanar nonlinear oscillation of a cantilever beam, the computation method is applied to compute the coefficients of the normal forms for the case of one non-semisimple double zero and a pair of pure imaginary eigenvalues.
- Publication:
-
Computational Mechanics and the Enhancement and Promotion of Computational Methods in Engineering and Science
- Pub Date:
- May 2010
- DOI:
- 10.1063/1.3452260
- Bibcode:
- 2010AIPC.1233..696C
- Keywords:
-
- nonlinear dynamical systems;
- Poincare mapping;
- functional analysis;
- 05.45.Pq;
- 11.30.Cp;
- 02.30.Sa;
- Numerical simulations of chaotic systems;
- Lorentz and Poincare invariance;
- Functional analysis