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.