  We study two-dimensional chaotic standard maps coupled along the edges of
scale-free trees and tree-like subgraph (4-star) with a non-symplectic coupling
and time delay between the nodes. Apart from the chaotic and regular 2-periodic
motion, the coupled map system exhibits variety of dynamical effects in a wide
range of coupling strengths. This includes dynamical localization, emergent
periodicity, and appearance of strange non-chaotic attractors. Near the strange
attractors we find long-range correlations in the intervals of return-times to
specified parts of the phase space. We substantiate the analysis with the
finite-time Lyapunov stability. We also give some quantitative evidence of how
the small-scale dynamics at 4-star motifs participates in the genesis of the
collective behavior at the whole network.
