There has been much interest in understanding collective dynamics in networks of brain regions due to their role in behavior and cognitive function. Here we show that a simple, homogeneous system of densely connected oscillators, representing the aggregate activity of local brain regions, can exhibit a rich variety of dynamical patterns emerging via spontaneous breaking of permutation or translational symmetries. Upon removing just a few connections, we observe a striking departure from the mean-field limit in terms of the collective dynamics, which implies that the sparsity of these networks may have very important consequences. Our results suggest that the origins of some of the complicated activity patterns seen in the brain may be understood even with simple connection topologies.
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We thank Raghavendra Singh, Purusattam Ray, Gautam Menon, Varsha Sreenivasan, V. Sasidevan and K. A. Chandrashekar for helpful discussions. We thank IMSc for providing access to the “Annapurna” supercomputer. This research was supported in part by the IMSc Complex Systems Project.