Abstract
It is known that intra-layer adaptive coupling among connected oscillators instigates explosive synchronization (ES) in multilayer networks. Taking an altogether different cue in the present work, we consider inter-layer adaptive coupling in a multiplex network of phase oscillators and show that the scheme gives rise to ES with an associated hysteresis irrespective of the network architecture of individual layers. The hysteresis is shaped by the inter-layer coupling strength and the frequency mismatch between the mirror nodes. We provide rigorous mean-field analytical treatment for the measure of global coherence and manifest they are in a good match with respective numerical assessments. Moreover, the analytical predictions provide a complete insight into how adaptive multiplexing suppresses the formation of a giant cluster, eventually giving birth to ES. The study will help in spotlighting the role of multiplexing in the emergence of ES in real-world systems represented by multilayer architecture. Particularly, it is relevant to those systems which have limitations towards change in intra-layer coupling strength.
Highlights
An irreversible synchronization process, called explosive synchronization (ES), in which a group of incoherent dynamical units are abruptly set in collective coherent motion, has drawn much attention of researchers [1,2]
In forward and backward continuation of coupling, output phases at coupling σ are used as initial phases at couplings σ + dσ and σ − dσ, respectively, where dσ represents a small change in the coupling strength
It is known that in a system of networked oscillators any microscopic strategy which can suppress the formation of the giant cluster can eventually lead to ES
Summary
An irreversible synchronization process, called explosive synchronization (ES), in which a group of incoherent dynamical units are abruptly set in collective coherent motion, has drawn much attention of researchers [1,2]. An isolated network is an unfit candidate to model such systems Such systems can be precisely framed by a multiplex network, where different layers denoting different dynamical processes are interconnected by the same set of nodes [19,20,21,22,23,24,25,26,27,28], for instance, social networks, neuronal networks, and transport systems in which individuals, neurons, and cities have different types of connections among them, each type forming a different layer [29]. It has been reported that the occurrence of ES in a multilayer network is exhibited by a fraction of nodes which are adaptively coupled via local order parameters within the multiplexed layers, having virtual interlayer links [15]. We corroborate our findings by providing rigorous mean-field analysis and show a good match between the analytical prediction of the order parameter and its numerical evaluation
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