Oscillation quenching mechanisms: Amplitude vs. oscillation death

Oscillation quenching constitutes a fundamental emergent phenomenon in systems of coupled nonlinear oscillators. Its importance for various natural and man-made systems, ranging from climate, lasers, chemistry and a wide range of biological oscillators can be projected from two main aspects: (i) suppression of oscillations as a regulator of certain pathological cases and (ii) a general control mechanism for technical systems. We distinguish two structurally distinct oscillation quenching types: oscillation ( O D ) and amplitude death ( A D ) phenomena. In this review we aim to set clear boundaries between these two very different oscillation quenching manifestations and demonstrate the importance for their correct identification from the aspect of theory as well as of applications. Moreover, we pay special attention to the physiological interpretation of O D and A D in a large class of biological systems, further underlying their different properties. Several open issues and challenges that await further resolving are also highlighted.