1-3hit |
Antonio ALGABA Manuel MERINO Alejandro J. RODRIGUEZ-LUIS
In this paper we study the evolution of the resonance zones that appear in connection with a Hopf-pitchfork bifurcation exhibited by a Z2-symmetric electronic circuit. These regions, bounded by curves of folds (saddle-node bifurcations) may be closed or open depending on the values of the parameters. An angular degeneracy on the torus bifurcation curve originates the banana shape of Arnold's tongues. The presence of homoclinic bifurcations is also pointed out.
Antonio ALGABA Emilio FREIRE Estanislao GAMERO Alejandro J. RODRIGUEZ-LUIS
The analysis of the Takens-Bogdanov bifurcation of the equilibrium at the origin in the Chua's equation with a cubic nonlinearity is carried out. The local analysis provides, in first approximation, different bifurcation sets, where the presence of several dynamical behaviours (including periodic, homoclinic and heteroclinic orbits) is predicted. The local results are used as a guide to apply the adequate numerical methods to obtain a global understanding of the bifurcation sets. The study of the normal form of the Takens-Bogdanov bifurcation shows the presence of a degenerate (codimension-three) situation, which is analyzed in both homoclinic and heteroclinic cases.
Antonio ALGABA Cristobal GARCIA Manuel MAESTRE Manuel MERINO
The main objective of this work is to provide a deep understanding of the periodic behaviour corresponding to a homoclinic related to the Takens-Bogdanov (double-zero eigenvalue of the linearization matrix) and the periodic behaviour of the torus bifurcation related to the Hopf-Pitchfork bifurcation (a pair of imaginary eigenvalues and the third one zero) corresponding to some sections of a triple-zero eigenvalue bifurcation in the Chua's equation with a cubic nonlinearity.