What is the name for a bifurcation where the signs of the eigenvalues switch?
E.g. Given a 4-dimensional saddle (two positive, two negative real eigenvalues), as I bifurcate a parameter two eigenvalues approach zero and cross zero simultaneously. Therefore at all times during the bifurcation of this parameter there are two positive and two negative eigenvalues, except the instance at which two are zero, one is positive and the other negative.
Is there a name for this behavior?
(I expect the symmetry in the problem, (i.e. the two eigenvalues symmetrically approaching zero together then passing through zero) arises from separation of variables of a single second order ODE into two first order ODEs.)