We investigate synchronization between two discrete-time networks with mutualcouplings, including inner synchronization inside each network and outer synchronization between two networks. We then obtain a synchronized criterion for the inner synchronization inside each network by themethod of linear matrix inequality and derive a relationship between the inner and outer synchronization. Finally, we show numerical examples to verify our theoretical analysis and discuss the effect of couplingstrengths, node dynamics, and topological structures on the inner and outer synchronization. Compared tothe inner synchronization inside each network, the outer synchronization between two networks is difficult toachieve.
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