Dynamics of multilayer networks with amplification

TL;DR

This paper investigates how amplification influences the dynamics of multilayer networks of chaotic oscillators, revealing phenomena like synchronization, chimera, and cluster states across different oscillator types and coupling configurations.

Contribution

It introduces the effect of amplification in multilayer chaotic oscillator networks and explores diverse dynamical states, including synchronization and chimera states, using various oscillator models and coupling topologies.

Findings

Amplification affects synchronization states in multilayer chaotic networks.

Chimera and cluster states can be induced or modified by amplification.

Synchronization can be suppressed or enhanced depending on parameters and amplification.

Abstract

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.