  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 system's 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.
