Generalizing the transition from amplitude to oscillation death in coupled oscillators

Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching types in coupled nonlinear oscillators. The transition from AD to OD has been recently realized due to the interplay between heterogeneity and coupling strength [A. Koseska et al., Phys. Rev. Lett. 111, 024103 (2013)]. We identify here the transition from AD to OD in nonlinear oscillators with couplings of distinct natures. It is demonstrated that the presence of time delay in the coupling cannot induce such a transition in identical oscillators, but it can indeed facilitate its occurrence with a low degree of heterogeneity. Moreover, it is further shown that the AD to OD transition is reliably observed in identical oscillators with dynamic and conjugate couplings. The coexistence of AD and OD and rich stable OD configurations after the transition are revealed, which are of great significance for potential applications in physics, biology, and control studies.