Fold and Homoclinic bifurcation

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I have a question of the positioning of bifurcation lines in 2D-parameterspace.

say we have a system of ODE's with two bifurcation parameters.

My understanding of the bifurcation lines is that the Fold line should contain the Homoclinic, and that they only tangentially meet in a Takens Bogdanov bifurcation point, but don't cross.

Is this true?