On the Takens-Bogdanov bifurcation in the Chua's equation

The analysis of the Takens-Bogdanov bifurcation of the equilibrium at the o rigin 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, h omoclinic and heteroclinic orbits) is predicted. The local results are used as a guide to apply the adequate numerical methods to obtain a global unde rstanding of the bifurcation sets. The study of the normal form of the Take ns-Bogdanov bifurcation shows the presence of a degenerate (codimension-thr ee) situation, which is analyzed in both homoclinic and heteroclinic cases.