  We study numerically synchronization phenomena of spatiotemporal structures,
including chimera states, in a two layer network of nonlocally coupled
nonlinear chaotic discrete-time systems. Each of the interacting ensembles
represents a one layer ring network of nonlocally coupled logistic maps in the
chaotic regime. The coupled networks differ in their control parameters that
enables one to observe distinct spatiotemporal dynamics in the networks when
there is no coupling between them. We explore in detail external and mutual
synchronization of chimera structures. The identity of synchronous structures
and the estimation of synchronization regions are quantified by calculating the
cross-correlation coefficient between relevant oscillators of the networks. We
show that for non-identical networks, unidirectional and symmetric couplings
lead to external and mutual synchronization between the interacting ensembles,
respectively. This is confirmed by identical synchronous structures and by the
existence of finite regions of synchronization within which the
cross-correlation coefficient is equal to 1. We also show that these findings
are qualitatively equivalent to the results of the classical synchronization
theory of periodic self-sustained oscillations.
