  We present a set of phase-space portraits illustrating the extraordinary
oscillatory possibilities of the dynamical systems through the so-called
generalized Landau scenario. In its simplest form the scenario develops in N
dimensions around a saddle-node pair of fixed points experiencing successive
Hopf bifurcations up to exhausting their stable manifolds and generating N-1
different limit cycles. The oscillation modes associated with these cycles
extend over a wide phase-space region by mixing ones within the others and by
affecting both the transient trajectories and the periodic orbits themselves. A
mathematical theory covering the mode-mixing mechanisms is lacking, and our aim
is to provide an overview of their main qualitative features in order to
stimulate research on it.
