Amplitude death in multiplex networks with competing attractive and repulsive interactions

Amplitude death (AD) phenomenon is one of the most striking and ubiquitous collective behaviors of coupled dynamical networks, in which all the dynamical units will cease their oscillations totally when the coupling occurs. Various appealing works have been devoted to the study of AD in the single-layer networks from theoretical and experimental perspectives in the last decades. However, it is still unclear under which conditions AD can be induced in the multiplex networks. In this work, we investigate the onset of AD of coupled systems connected via multiplex network architectures in the presence of competing attractive and repulsive intralayer and interlayer interactions. We first theoretically derive the critical condition of AD for a class of generalized multiplex network models. Then we apply it to calculate the stable AD regions for the case of a single-layer network of Stuart–Landau oscillators and observe that in the single-layer ring network, AD only can occur for small networks regardless of how to tune the proportion of repulsive coupling. Whereas, for the single-layer all-to-all network, AD always can appear, and the larger the network size or the proportion of repulsive coupling, the smaller the required coupling strength for AD is. Finally, we show in the three-layer multiplex network of Stuart–Landau oscillators that the stable AD regions can be concluded to four types based on the intralayer and interlayer network topologies. In particular, even if AD does not exist separately in each layer network, it can be reached by choosing appropriately interlayer interaction in the three-layer multiplex network. Our study sheds a new insight into the generation of AD phenomenon and gives a general framework to analyze the steady state behaviors of coupled systems in the multiplex networks.