Comovement of economic activity across sectors and countries is a defining
feature of business cycles. However, standard models that attribute comovement
to propagation of exogenous shocks struggle to generate a level of comovement
that is as high as in the data. In this paper, we consider models that produce
business cycles endogenously, through some form of non-linear dynamics---limit
cycles or chaos. These models generate stronger comovement, because they
combine shock propagation with synchronization of endogenous dynamics. In
particular, we study a demand-driven model in which business cycles emerge from
strategic complementarities across sectors in different countries,
synchronizing their oscillations through input-output linkages. We first use a
combination of analytical methods and extensive numerical simulations to
establish a number of theoretical results. We show that the importance that
sectors or countries have in setting the common frequency of oscillations
depends on their eigenvector centrality in the input-output network, and we
develop an eigendecomposition that explores the interplay between non-linear
dynamics, shock propagation and network structure. We then calibrate our model
to data on 27 sectors and 17 countries, showing that synchronization indeed
produces stronger comovement, giving more flexibility to match the data