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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 Rössler chaotic oscillators as well as applications to multilayer networks of chaotic jerk and Liénard oscillators. Intra-layer coupling is considered to be all to all in the case of Rössler oscillators, a ring for jerk oscillators and global mean field coupling in the case of Liénard, the inter-layer 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 Rössler 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 Rössler oscillators, we note that there are also certain values of coupling parameters and amplification where the synchronization doesn't 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.Research on multilayer networks has attracted a lot of attention in recent years in many areas of physics, engeneering, social sciences etc 1-6 . Some emergent behaviors in such systems due to interaction among the dynamical units reveal a variety of interesting phenomena, such as synchronization 1,7,8 , cluster formation 9 , explosive synchronization 10 , explosive desynchronization 11 , chimera 12-16 etc. Among these, synchronization and chimeras are the most widely studied. The notion of amplification is very important in science and technology. This work presents an investigation of different phenomena such as complete synchronization, cluster formation, phase synchronization and chimera states in a network with amplification. For an extended study we present three cases with three different topologies.

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