  A saddle to saddle-focus homoclinic transition when the stable leading
eigenspace is 3-dimensional (called the 3DL bifurcation) is analyzed. Here a
pair of complex eigenvalues and a real eigenvalue exchange their position
relative to the imaginary axis, giving rise to a 3-dimensional stable leading
eigenspace. This transition is different from the standard Belyakov
bifurcation, where a double real eigenvalue splits either into a pair of
complex-conjugate eigenvalues or two distinct real eigenvalues. In the wild
case, we obtain sets of codimension 1 and 2 bifurcation curves and points that
asymptotically approach the 3DL bifurcation point and have a structure that
differs from that the standard Belyakov case. We also give an example of this
bifurcation in the wild case occuring in a perturbed Lorenz-Stenflo 4D ODE
model.
