Abstract
We investigate the synchronization of time-delayed complex dynamical networks with periodic on-off coupling. We derive sufficient conditions for the complete and generalized outer synchronization. Both our analytical and numerical results show that two time-delayed networks can achieve outer synchronization even if the couplings between the two networks switch off periodically. This synchronization behavior is largely dependent of the coupling strength, the on-off period, the on-off rate and the time delay. In particular, we find that the synchronization time nonmonotonically increases as the time delay increases when the time delay step is not equal to an integer multiple of the on-off period.
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