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Abstract Recent analyses have found waves of neural activity traveling across entire visual cortical areas in awake animals. These traveling waves modulate the excitability of local networks and perceptual sensitivity. The general computational role of these spatiotemporal patterns in the visual system, however, remains unclear. Here, we hypothesize that traveling waves endow the visual system with the capacity to predict complex and naturalistic inputs. We present a network model whose connections can be rapidly and efficiently trained to predict individual natural movies. After training, a few input frames from a movie trigger complex wave patterns that drive accurate predictions many frames into the future solely from the network’s connections. When the recurrent connections that drive waves are randomly shuffled, both traveling waves and the ability to predict are eliminated. These results suggest traveling waves may play an essential computational role in the visual system by embedding continuous spatiotemporal structures over spatial maps. 

One of the simplest mathematical models in the study of nonlinear systems is the Kuramoto model, which describes synchronization in systems from swarms of insects to superconductors. We have recently found a connection between the original, real-valued nonlinear Kuramoto model and a corresponding complex-valued system that permits describing the system in terms of a linear operator and iterative update rule. We now use this description to investigate three major synchronization phenomena in Kuramoto networks (phase synchronization, chimera states, and traveling waves), not only in terms of steady state solutions but also in terms of transient dynamics and individual simulations. These results provide new mathematical insight into how sophisticated behaviors arise from connection patterns in nonlinear networked systems.