  This paper addresses the synchronized region problem, which is reduced to a
matrix stability problem, for complex dynamical networks. For any natural
number $n$, the existence of a network which has $n$ disconnected synchronized
regions is theoretically demonstrated. This shows the complexity in network
synchronization. Convexity characteristic of stability for matrix pencils is
further discussed. Smooth and generalized smooth Chua's circuit networks are
finally discussed as examples for illustration.
