Multiplexing noise induces synchronization in multilayer networks

We study numerically the spatio-temporal behavior of a two-layer multiplex network of bistable cubic maps when the interlayer coupling is modulated by noise. We refer to this interlayer coupling noise as a multiplexing noise. Various spatio-temporal structures can be established in the uncoupled layers depending on initial conditions. They may represent chimeras of different forms, spatially irregular patterns or spatially homogeneous states. The interlayer coupling strength between the mirror nodes of the layers is given by independent sources of Gaussian colored noise with identical characteristics. We explore the evolution of the spatio-temporal dynamics of the interacting layers when the multiplexing noise parameters are varied. The network dynamics is considered in the case of identical and nonidentical layers which differ in the intralayer coupling strength. It is shown that the low-frequency multiplexing noise produces the solitary states in the networks. The nodes which are in these solitary states have a special temporal dynamics which is revealed for the first time. It is demonstrated that complete and close to complete synchronization of the layers can be achieved at certain characteristics of the noise sources. We analyze how synchronization depends on the initial regimes of two layers. Diagrams are constructed that reflect the degree of layer synchronization in the plane of parameters that control the spectrum and intensity of noise sources.