  When nonlinear dynamical systems are coupled, depending on the intrinsic
dynamics and the manner in which the coupling is organized, a host of novel
phenomena can arise. In this context, an important emergent phenomenon is the
complete suppression of oscillations, formally termed amplitude death (AD).
Oscillations of the entire system cease as a consequence of the interaction,
leading to stationary behavior. The fixed points that the coupling stabilizes
can be the otherwise unstable fixed points of the uncoupled system or can
correspond to novel stationary points. Such behaviour is of relevance in areas
ranging from laser physics to the dynamics of biological systems. In this
review we discuss the characteristics of the different coupling strategies and
scenarios that lead to AD in a variety of different situations, and draw
attention to several open issues and challenging problems for further study.
