Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps

Abstract We numerically study the spatiotemporal dynamics of a heterogeneous two-layer network of chaotic discrete-time systems. The multiplex network is described by uni- or bidirectionally coupled rings of Henon and Lozi maps with a nonlocal interaction. We examine in detail effects of weakly and strongly sparse inter-layer coupling upon effective synchronization and compare with the network dynamics in the case of non-sparse coupling between the rings. We show for the first time that effective synchronization is confidently observed in a finite range on the inter-layer coupling strength even when up to 50% links between the rings are missing. The impact of a different degree of sparseness of the inter-layer coupling is quantified by using the global synchronization measure. We also analyze the contribution of the intra- and inter-layer couplings in the synchronous structure formation.