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Homoclinic Interactions Near a Triple-Zero Degeneracy in Chua's equation

In this work, we consider some degeneracies of homoclinic and heteroclinic connections organized by the triple-zero degeneracy, in Chua's equation. This allows us to numerically study the homoclinic-heteroclinic transition exhibited by the curve of Takens–Bogdanov bifurcations as it passes through the triple-zero degeneracy. Several codimension-two degenerate homoclinic and heteroclinic connections organized by the triple-zero bifurcation are involved in this transitional homoclinic-heteroclinic mechanism. In particular, we point out that the existence of a curve of T-points and a curve of Belyakov points (its equilibrium passes from saddle to saddle-focus) is necessary for this process to occur. Closed curves of homoclinic connections with different pulses are also found.