Synchronization is one of the most fascinating phenomena across the natural and social sciences. It is the tendency of systems as diverse as oscillating pendula, flashing fireflies, firing neurons, and applauding audiences to align their non-linear dynamics in a way that they operate in synchrony. Despite the many applications of synchronization theory, so far it has had little impact in economics. This is due to three main reasons: (i) supposed evidence against non-linear dynamics in economic time series; (ii) difficulty to associate economic mechanisms to workhorse models of synchronization; (iii) relatively little attention to exogenous shocks in synchronization theory. In this project, we address these issues by developing a demand-driven, non-linear model of endogenous business cycles. In this model, economic sectors in various countries adjust their frequencies of oscillation to one another through input-output linkages. Sectors like manufacturing and countries like the US have the largest power to set the frequencies of oscillation. We develop a theory that analytically explores the interplay between non-linear dynamics, shock propagation and network structure. This model is consistent with a concentration of periodicities around 10 years and with some correlation patterns of several economic variables across 17 advanced economies and 27 sectors. It proposes a new mechanism for the micro origin of aggregate fluctuations and for the international synchronization of business cycles, further develops the theory of endogenous business cycles and networks in economics and, more broadly, extends some results in synchronization theory by analyzing a new type of system.