We review the research on complex dynamical networks (CDNs) with impulsive effects. We provide a comprehensive and intuitive overview of the fundamental results and recent progress of CDNs with impulsive effects, where impulsive effects are considered from two aspects, i.e., impulsive control and impulsive perturbation. Five aspects of CDNs with impulsive effects are surveyed, including synchronizing impulses, desynchronizing impulses, adaptive-impulsive synchronization, pinning impulsive synchronization, and CDNs with stochastic and impulsive effects. Finally, conclusions and some future research directions are briefly addressed.
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