Emergence of synchronization in multiplex networks of mobile R\"{o}ssler oscillators

TL;DR

This paper investigates how synchronization emerges in multiplex networks of mobile Rössler oscillators with time-varying connections, analyzing the effects of mobility and coupling parameters on the stability and robustness of synchronized states.

Contribution

It introduces a comprehensive study of synchronization in mobile multiplex networks, combining numerical simulations with analytical conditions, and explores robustness under structural and dynamical perturbations.

Findings

Interlayer synchronization can be maintained despite link removal.

Mobility parameters can restore synchronization after structural disruptions.

Synchronization stability is influenced by network parameters and mobility dynamics.

Abstract

Different aspects of synchronization emerging in dynamical networks of coupled oscillators have been examined prominently in the last decades. Nevertheless, little attention has been paid on the emergence of this imperative collective phenomenon in networks displaying temporal changes in the connectivity patterns. However there are numerous practical examples where interactions are present only at certain points of time owing to physical proximity. In this work, we concentrate on exploring the emergence of interlayer and intralayer synchronization states in a multiplex dynamical network comprising of layers having mobile nodes performing a random walk. We thoroughly illustrate the impacts of the network parameters, in particular the vision range $\phi$ and the step size $u$ together with the inter- and intralayer coupling strengths $\epsilon$ and $k$ on these synchronous states arising in coupled R\"{o}ssler systems. The presented numerical results are very well validated by analytically derived necessary conditions for the emergence and stability of the synchronous states. Furthermore, the robustness of the states of synchrony is studied under both structural and dynamical perturbations. We find interesting results on interlayer synchronization for a continuous removal of the interlayer links as well as for progressively created static nodes. We demonstrate that the mobility parameters responsible for intralayer movement of the nodes, can retrieve interlayer synchrony under such structural perturbations. For further analysis of survivability of interlayer synchrony against dynamical perturbations, we proceed through the investigation of single-node basin stability, where again the intralayer mobility properties have noticeable impacts. We also discuss the scenarios related mainly to effects of the mobility parameters in terms of percolation of the whole network.