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We study numerically synchronization phenomena of spatiotemporal structures,including chimera states, in a two layer network of nonlocally couplednonlinear chaotic discrete-time systems. Each of the interacting ensemblesrepresents a one layer ring network of nonlocally coupled logistic maps in thechaotic regime. The coupled networks differ in their control parameters thatenables one to observe distinct spatiotemporal dynamics in the networks whenthere is no coupling between them. We explore in detail external and mutualsynchronization of chimera structures. The identity of synchronous structuresand the estimation of synchronization regions are quantified by calculating thecross-correlation coefficient between relevant oscillators of the networks. Weshow that for non-identical networks, unidirectional and symmetric couplingslead to external and mutual synchronization between the interacting ensembles,respectively. This is confirmed by identical synchronous structures and by theexistence of finite regions of synchronization within which thecross-correlation coefficient is equal to 1. We also show that these findingsare qualitatively equivalent to the results of the classical synchronizationtheory of periodic self-sustained oscillations.

External and mutual synchronization of chimeras in a two layer network of nonlinear oscillators