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Abstract

Rhythmic behavior represents one of the most striking and ubiquitous manifestations of functional evolution for a wide class of natural and man-made systems. The emergence of diverse (ar)rhythmic dynamics can be well understood by models of coupled dynamical networks, where the interplay between the intrinsic dynamics of a single unit and the coupling functions plays a critical role in shaping a vast repertoire of collective behaviors. Under certain circumstances, all the individual dynamical systems may cease their oscillations totally when coupled, which results in the emergence of oscillation quenching in coupled oscillatory systems. Macroscopic oscillations of coupled dynamical networks can also be gradually weakened and even completely quenched via aging transition. Oscillation reviving, an inverse process of quenching and aging, refers to the restoration of rhythmic activity of coupled dynamical networks from the phenomena of quenching and aging. The study on quenching, aging, and reviving of rhythmic behaviors in coupled dynamical networks has developed into an active and rapidly evolving area of research with a wide variety of applications, where tremendous progresses with vital insights have been witnessed in the last decade. In this review, we endeavour to provide an exhaustive overview on the most important aspects of quenching, aging, and reviving in coupled dynamical networks ranging from theories to experiments and applications. The prevailing knowledge is integrated and pulled together to make the relevant results and methods more generally accessible for researchers in distinct communities of science and technology. Relevant open issues and challenges that deserve of special attentions are highlighted for future study. The present review should stimulate deeper investigations on the collapse and revival of macroscopic rhythmic behaviors, which will enlighten our understanding on evading irreversible failures of coupled dynamical networks and even guide us to identify the precursors of critical transitions. Our work will foster further studies on the physical principles of collective rhythms that robustly emerge in nature and real life.