Diverse routes of transition from amplitude to oscillation death in coupled oscillators under additional repulsive link

Abstract: 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.