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The dynamics of coupled 2D chaotic maps with time-delay on a scalefree-treeis studied, with different types of the collective behaviors already beenreported for various values of coupling strength [1]. In this work we focus onthe dynamics' time-evolution at the coupling strength of the stabilitythreshold and examine the properties of the regularization process. Thetime-scales involved in the appearance of the regular state and the periodicstate are determined. We find unexpected regularity in the the system's finalsteady state: all the period values turn out to be integer multiples of oneamong given numbers. Moreover, the period value distribution follows apower-law with a slope of -2.24.

Dynamical Regularization in Scalefree-trees of Coupled 2D Chaotic Maps