# Synchronization in networks with multiple interaction layers

@article{delGenio2016SynchronizationIN, title={Synchronization in networks with multiple interaction layers}, author={Charo I. del Genio and Jes{\'u}s G{\'o}mez-Garde{\~n}es and Ivan Bonamassa and Stefano Boccaletti}, journal={Science Advances}, year={2016}, volume={2} }

When the coexistence of multiple types of interactions truly matters for the synchronization of interacting complex systems. The structure of many real-world systems is best captured by networks consisting of several interaction layers. Understanding how a multilayered structure of connections affects the synchronization properties of dynamical systems evolving on top of it is a highly relevant endeavor in mathematics and physics and has potential applications in several socially relevant…

## 101 Citations

### Mean-field nature of synchronization stability in networks with multiple interaction layers

- Computer ScienceCommunications Physics
- 2022

A mean-field theory of synchronization for networks with multiple interaction layers is developed and it is shown that this applies to both homogeneous and heterogeneous layers, lowering computational complexity.

### Mean-field nature of synchronization stability in networks with multiple interaction layers

- Computer ScienceCommunications Physics
- 2022

A mean-field theory of synchronization for networks with multiple interaction layers is developed and it is shown that this applies to both homogeneous and heterogeneous layers, lowering computational complexity.

### When multilayer links exchange their roles in synchronization.

- Computer SciencePhysical review. E
- 2022

An approximation method is proposed which significantly enhances the predictive power of the master stability function for stable synchronization in multilayer networks and reduces the complex stability analysis to simply solving a set of linear algebraic equations for saddle-focus oscillators.

### Stability of synchronization in simplicial complexes with multiple interaction layers.

- Computer SciencePhysical review. E
- 2022

It is shown that the synchronization state exists as an invariant solution and derive the necessary condition for a stable synchronization state in the presence of general coupling functions and is generalizes the well-known master stability function scheme to higher-order structures with multiple interaction layers.

### Dynamics of multilayer networks with amplification.

- PhysicsChaos
- 2020

Using other systems with different topologies, an in-depth study on the case of a network of Rössler oscillators using a master stability function and order parameter leads to several phenomena such as complete synchronization, generalized, cluster, and phase synchronization with amplification.

### Emergence of synchronization in multiplex networks of mobile Rössler oscillators.

- Computer SciencePhysical review. E
- 2019

This work concentrating on exploring the emergence of interlayer and intralayer synchronization states in a multiplex dynamical network comprising of layers having mobile nodes performing two-dimensional lattice random walk finds interesting results on interlayer synchronization for a continuous removal of the interlayer links as well as for progressively created static nodes.

### Stability of synchronization in simplicial complexes

- Computer ScienceNature Communications
- 2021

It is shown that complete synchronization exists as an invariant solution, and the necessary condition for it to be observed as a stable state is given, and in some relevant instances, such a necessary condition takes the form of a Master Stability Function.

### Inter-layer synchronization in non-identical multi-layer networks

- Computer ScienceScientific Reports
- 2017

By the use of multiplexed layers of electronic circuits, the inter-layer synchronization as a function of the removed links is studied, and a non-trivial relationship connecting the betweenness centrality of the missing links and the intra-layer coupling strength is identified.

### Symmetry-Independent Stability Analysis of Synchronization Patterns

- Computer ScienceSIAM Rev.
- 2020

A generalization of the MSF formalism is established that can characterize the stability of any cluster synchronization pattern, even when the oscillators and/or their interactions are nonidentical, and leads to an algorithm that is error-tolerant and orders of magnitude faster than existing symmetry-based algorithms.

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