  We report the existence of diverse routes of transition from amplitude death
(AD) to oscillation death (OD) in three different diffusively coupled systems,
those are perturbed by a symmetry break- ing repulsive coupling link. For limit
cycle systems the transition is through a pitchfork bifurcation (PB) as has
been noted before, but in chaotic systems it can be through a saddle-node or a
trans- critical bifurcation depending on the nature of the underlying dynamics
of the individual systems. The diversity of the routes and their dependence on
the complex dynamics of the coupled systems not only broadens our understanding
of this important phenomenon but can lead to potentially new practical
applications.
