  We study the dynamics of a multilayer network of chaotic oscillators subject
to an amplification. Previous studies have proven that multilayer networks
present phenomena such as synchronization, cluster and chimera states. Here we
consider a network with two layers of Roessler chaotic oscillators as well as
applications to multilayer networks of chaotic jerk and Lienard oscillators.
Intralayer coupling is considered to be all to all in the case of Roessler
oscillators, a ring for jerk oscillators and global mean field coupling in the
case of Lienard, the interlayer coupling is unidirectional in all these three
cases. The second layer has an amplification coefficient. An in depth study on
the case of a network of Roessler oscillators using master stability function
and order parameter leads to several phenomena such as complete
synchronization, generalized, cluster and phase synchronization with
amplification. For the case of Roessler oscillators, we note that there are
also certain values of coupling parameters and amplification where the
synchronization does not exist or the synchronization can exist but without
amplification. Using other systems with different topologies, we obtain some
interesting results such as chimera state with amplification, cluster state
with amplification and complete synchronization with amplification.
