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Abstract

Complex networks of dynamically connected saddle states persistently emerge in a broad range of high-dimensional systems and may reliably encode inputs as specific switching trajectories. Their computational capabilities, however, are far from being understood. Here, we analyze how symmetry-breaking inhomogeneities naturally induce predictable persistent switching dynamics across such networks. We show that such systems are capable of computing arbitrary logic operations by entering into switching sequences in a controlled way. This dynamics thus offers a highly flexible new kind of computation based on switching along complex networks of states.