  Recently, the synchronization on multi-layer networks has drawn a lot of
attention. In this work, we study the stability of the complete synchronization
on duplex networks. We investigate effects of coupling function on the complete
synchronization on duplex networks. We propose two approximation methods to
deal with the stability of the complete synchronization on duplex networks. In
the first method, we introduce a modified master stability function and, in the
second method, we only take into consideration the contributions of a few most
unstable transverse modes to the stability of the complete synchronization. We
find that both methods work well for predicting the stability of the complete
synchronization for small networks. For large networks, the second method still
works pretty well.

Chaotic Dynamics