Emergence of synchronization in multiplex networks of mobile Rössler oscillators

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 φ and the step size u together with the inter-and intralayer coupling strengths and k on these synchronous states arising in coupled Rössler 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.

Two classes of functional connectivity in dynamical processes in networks

“…Another direction of extending our investigation is to have continuous chaotic systems. Here, the Lorenz system [259,260], Rössler system [261,262] or Stuart-Landau system [263,264] would be suitable candidates. The question is then, how the results described above change when going from discrete to continuous time and when going from a one-dimensional system (at each node) to a higher-dimensional system.…”

Synchronization to extreme events in moving agents

“…In this paper, we consider a planar space in which some identical moving chaotic oscillators interact with each other only when they visit the same restricted regions pre-defined in the planar zone. This interactional platform is thus different from most of the existing studies [19,[34][35][36][37]41] in the field on synchronization of moving agents till now, in which each moving agent is associated with an interaction zone that moves with the agent.…”

“…robots [19], ordered motion in a group of animals [20] and even in the process of chemotaxis [21], this framework has a significant resemblance. Emergence of complete synchronization from different aspects in temporal networks [22][23][24][25][26][27][28][29][30][31][32], particularly among interacting moving oscillators has been investigated previously [19,[33][34][35][36][37][38][39][40][41] and most of these articles considered the framework in which each and every agent always carries a vision shape based on which they create neighbors and interact. In this paper, we consider a planar space in which some identical moving chaotic oscillators interact with each other only when they visit the same restricted regions pre-defined in the planar zone.…”

Enhancing synchrony in multiplex network due to rewiring frequency

“…Among them, one pioneering explorations are synchronization properties [8,9] of coupled network and these phenomena have been mostly studied in the last few decades for its immense applicability in various physical [10] and engineered systems [11]. Previously, different types of synchrony properties have been studied in multiplex network organization such as cluster synchronization [12], interlayer synchronization [13,14], intralayer synchronization [15][16][17], the coexistence of synchrony and asynchrony [18][19][20], and explosive synchronization [21]. But in most cases, the network structures are considered as static networks which means that the underlying connections are invariant with respect to time.…”