Abstract
We study two-dimensional chaotic standard maps coupled along the edges of scale-freetrees and tree-like subgraphs (4-star) with a non-symplectic coupling and time delaybetween the nodes. Apart from the chaotic and regular 2-periodic motion, the coupledmap system exhibits a variety of dynamical effects in a wide range of couplingstrengths. This includes dynamical localization, emergent periodicity and theappearance of strange non-chaotic attractors. Near the strange attractors wefind long-range correlations in the intervals of return times to specified partsof the phase space. We substantiate the analysis with the finite-time Lyapunovstability. We also give some quantitative evidence of how the small-scale dynamics at4-star motifs participates in the genesis of the collective behavior at the wholenetwork.
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