Interlayer adaptation-induced explosive synchronization in multiplex networks

Abstract

It is known that intralayer adaptive coupling among connected oscillators instigates explosive synchronization (ES) in multilayer networks. Taking an altogether different cue in the present work, we consider interlayer adaptive coupling in a two-layer multiplex network of phase oscillators and show that the scheme gives rise to ES with an associated hysteresis. The hysteresis is shaped by the interlayer coupling strength and the frequency mismatch between the mirror nodes. We provide a rigorous mean-field analytical treatment and show that the analytical predictions are in fair agreement with the numerical assessments. Moreover, the analytical predictions provide extensive insight into how adaptive interlayer coupling suppresses the formation of a giant cluster, eventually giving birth to ES. The study will help in spotlighting the role of interlayer adaptation in the emergence of ES in real-world systems represented by multilayer architecture. In particular, it is relevant to those systems which have limitations towards changes in intralayer coupling strength.