  We study the critical behaviors of period doublings in N (N=2,3,4,...)
coupled inverted pendulums by varying the driving amplitude $A$ and the
coupling strength $c$. It is found that the critical behaviors depend on the
range of coupling interaction. In the extreme long-range case of global
coupling, in which each inverted pendulum is coupled to all the other ones with
equal strength, the zero-coupling critical point and an infinity of critical
line segments constitute the same critical set in the $A-c$ plane,
independently of $N$. However, for any other nonglobal-coupling cases of
shorter-range couplings, the structure of the critical set becomes different
from that for the global-coupling case, because of a significant change in the
stability diagram of periodic orbits born via period doublings. The critical
scaling behaviors on the critical set are also found to be the same as those
for the abstract system of the coupled one-dimensional maps.
