Approximation methods for the stability of complete synchronization on duplex networks
arXiv:1707.01249 · doi:10.1016/j.chaos.2017.11.008
Abstract
Recently, the synchronization on multi-layer networks has drawn a lot of attention. In this work, we study the stability of the complete synchronization on duplex networks. We investigate effects of coupling function on the complete synchronization on duplex networks. We propose two approximation methods to deal with the stability of the complete synchronization on duplex networks. In the first method, we introduce a modified master stability function and, in the second method, we only take into consideration the contributions of a few most unstable transverse modes to the stability of the complete synchronization. We find that both methods work well for predicting the stability of the complete synchronization for small networks. For large networks, the second method still works pretty well.
6 pages, 6 figures
References in corpus (22)
- Catastrophic cascade of failures in interdependent networks
- Statistical physics of social dynamics
- Epidemic processes in complex networks
- Synchronization in complex networks
- Multilayer Networks
- The structure and dynamics of multilayer networks
- Evolutionary games on graphs
- Dynamical interplay between awareness and epidemic spreading in multiplex networks
- The physics of spreading processes in multilayer networks
- Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
- Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
- Entangled networks, synchronization, and optimal network topology
- Synchronization in networks with multiple interaction layers
- Synchronization of interconnected networks: the role of connector nodes
- Optimal synchronization of complex networks
- Synchronization of hypernetworks of coupled dynamical systems
- Inter-layer synchronization in multiplex networks
- Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles
- Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices
- Can we neglect the multi-layer structure of functional networks?
- Controlling synchronous patterns in complex networks
- Enhancing the stability of the synchronization of multivariable coupled oscillators