The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-tree is studied, with different types of the collective behaviors already been reported for various values of coupling strength [1]. In this work we focus on the dynamics time-evolution at the coupling strength of the stability threshold and examine the properties of the regularization process. The time-scales involved in the appearance of the regular state and the periodic state are determined. We find unexpected regularity in the the systems final steady state: all the period values turn out to be integer multiples of one among given numbers. Moreover, the period value distribution follows a power-law with a slope of -2.24.
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