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This implies that the origin of (3.3), that is, of (1.6), is a cusp of codimension by in [25, Theorem, Section ].
The equilibrium of (1.6) is a cusp of codimension if (H1) and (H2) hold; that is, it is a Bogdanov-Takens singularity.
It is interesting that they found that the unique equilibrium is a cusp of codimension 3 (a degenerate Bogdanov-Takens bifurcation point).
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CEO of Professional Science Editing for Scientists @ prosciediting.com