  Sets in the parameter space corresponding to complex exceptional points have
high codimension and by this reason they are difficult objects for numerical
localization. However, complex EPs play an important role in the problems of
stability of dissipative systems where they are frequently considered as
precursors to instability. We propose to localize the set of complex EPs using
the fact that the minimum of the spectral abscissa of a polynomial is attained
at the EP of the highest possible order. Applying this approach to the problem
of self-stabilization of a bicycle we find explicitly the EP sets that suggest
scaling laws for the design of robust bikes that agree with the design of the
known experimental machines
