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This paper considers the effects of forced and mutual synchronization of complex spatio-temporal structures in a two-layer network of nonlocally coupled logistic maps in the presence of inhomogeneous interlayer coupling. Two different types of coupling topology are considered: the first one is the sparse interlayer coupling with randomly distributed coupling defects, and the second type is the cluster interlayer coupling, providing the coupling via designated finite groups of elements. The latter type of coupling topology is considered for the first time. As a quantitative measure of the synchronization effect on the network, variance averaged over time and variance averaged both over time and network elements are used. We analyze how the synchronization measure changes depending on a degree of the interlayer coupling sparseness.We also identify a cluster of network elements which can provide almost complete synchronizationin the network under study when the interlayer coupling is introduced along them.

Peculiarities of Synchronization in a Two-Layer Network of Chaotic Maps with Inhomogeneous Interlayer Coupling