Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators
arXiv:1708.01883 · doi:10.1103/PhysRevE.96.042312
Abstract
This work considers the timescales associated with the global order parameter and the interlayer synchronization of coupled Kuramoto oscillators on multiplexes. For the two-layer multiplexes with initially high degree of synchronization in each layer, the difference between the average phases in each layer is analyzed from two different perspectives: the spectral analysis and the non-linear Kuramoto model. Both viewpoints confirm that the prior timescales are inversely proportional to the interlayer coupling strength. Thus, increasing the interlayer coupling always shortens the transient regimes of both the global order parameter and the interlayer synchronization. Surprisingly, the analytical results show that the convergence of the global order parameter is faster than the interlayer synchronization, and the latter is generally faster than the global synchronization of the multiplex. The formalism also outlines the effects of frequencies on the difference between the average phases of each layer, and identifies the conditions for an oscillatory behavior. Computer simulations are in fairly good agreement with the analytical findings and reveal that the timescale of the global order parameter is at least half times smaller than timescale of the multiplex.
26 pages, 9 figures
References in corpus (15)
- The structure and dynamics of multilayer networks
- Diffusion dynamics on multiplex networks
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Multirelational Organization of Large-scale Social Networks in an Online World
- Emergence of network features from multiplexity
- MuxViz: A Tool for Multilayer Analysis and Visualization of Networks
- Modeling the Multi-layer Nature of the European Air Transport Network: Resilience and Passengers Re-scheduling under random failures
- Degree mixing in multilayer networks impedes the evolution of cooperation
- Synchronization in networks with multiple interaction layers
- Pattern formation in multiplex networks
- Synchronization processes in complex networks
- Turing patterns in multiplex networks
- Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
- Dynamical and spectral properties of complex networks
- Strategical incoherence regulates cooperation in social dilemmas on multiplex networks