In the theory of singularly perturbed initial‐value problems, the principal assumption concerns a certain Jacobian matrix: all its eigenvalues should have negative real parts at each point of the reduced (or degenerate) path. If the reduced path contains a point of bifurcation, this assumption is violated. The simplest kind of bifurcation with exchange of stabilities involves just two smooth curves intersecting at a single point. The analysis of the singular perturbation theory in the case when bifurcation is present depends on whether or not both curves have finite slopes at the point of bifurcation. The case when both slopes are finite was treated in [1]; the case when the bifurcating curve has a vertical tangent is treated in the present paper.
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