trajectories amplification in multilayer networks

The amplification phenomenon in chaotic systems was first observed and studied by J. M. Gonzalez

- Miranda in Ref.[1] where she found that amplification and displacement of chaotic attractors by

means of unidirectional chaotic driving. Later I. Grosu et al. in Ref.[2], proposed a design of coupling

for stable synchronization and antisynchronization in chaotic systems under parameter mismatch.

They end their work with an experimental set up showing the effectiveness of their study. The present

work goal is to investigate the trajectories amplification in multilayer networks. Basing ourselves on

the coupling method proposed in Ref.[3, 4], we will investigate conditions within which the coupled

networks can achieve synchronization and amplification (reduction). These investigations will be

carried out for both non mobile and mobile oscillators. Synchronization analysis will be investigated

using master stability function in the driver network, the order parameter in the response network

while the transverse Lyapunov exponent will be applied between corresponding oscillators in each

network. The effectiveness of the investigation is shown when network are incoherent, synchronized

and even in chimera state.