# Universality in the synchronization of weighted random networks.

@article{Zhou2006UniversalityIT, title={Universality in the synchronization of weighted random networks.}, author={Changsong Zhou and Adilson E. Motter and J{\"u}rgen Kurths}, journal={Physical review letters}, year={2006}, volume={96 3}, pages={ 034101 } }

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a…

## 276 Citations

Synchronizing weighted complex networks.

- Mathematics, MedicineChaos
- 2006

This work considers a coupling scheme in which the relative importance of a link depends on the number of shortest paths through it, and investigates the constructive role played by such a directed and weighted wiring for the synchronization of networks of coupled dynamical systems.

Dynamical weights and enhanced synchronization in adaptive complex networks.

- Computer Science, MedicinePhysical review letters
- 2006

It is found that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks.

Synchronization in a class of weighted complex networks with coupling delays

- Computer Science
- 2008

On the basis of the theory of asymptotic stability of linear time-delay systems with complex coefficients, the synchronization stability of weighted complex dynamical networks with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of the synchronization state.

Synchronization Stability in Weighted Complex Networks with Coupling Delays

- Computer Science
- 2009

Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states.

THE MANY FACES OF SYNCHRONIZATION OF NETWORKS

- Computer Science
- 2009

This work clarifies that although the eigen ratio is relevant to the possible range of coupling strength for achieving synchronization, it cannot fully determine the latter and plays a decisive role in the interpretation of synchronizability.

Synchronization Probability in Large Complex Networks

- Mathematics, PhysicsIEEE Transactions on Circuits and Systems II: Express Briefs
- 2013

A sufficient condition for the stability of synchronization is derived, which explicitly relates the network structure and the local and coupling dynamics to synchronization stability, and is translated into a lower bound on the probability of stability of synchrony for large Erdös-Rényi and Newman-Watts small-world networks.

Synchronization-based scalability of complex clustered networks.

- Mathematics, MedicineChaos
- 2008

Theoretical analysis and numerical computations reveal that, for a typical clustered network, as its size is increased, the synchronizability can be maintained or even enhanced but at the expense of deterioration of the clustered characteristics in the topology that distinguish this type of networks from other types of complex networks.

The development of generalized synchronization on complex networks.

- Mathematics, PhysicsChaos
- 2009

This paper numerically investigates the development of generalized synchronization on typical complex networks, such as scale-free networks, small-world networks, random networks, and modular networks and observes that GS generally takes place in oscillator networks with both heterogeneous and homogeneous degree distributions, regardless of whether the coupled chaotic oscillators are identical or nonidentical.

Homogeneity of Load Distribution Plays a Key Role in Global Synchronizability of Complex Networks

- Computer Science
- 2008

Based on the coupled oscillator model, it is found that the homogeneity of load distribution determines the synchronizability of complex networks, and the standard deviation of edge betweenness centrality is coincident with synchronizeability for various complex networks.

Synchronization of Kuramoto oscillators in random complex networks

- Computer Science
- 2008

The synchronizability of coupled oscillators can be enhanced in ER networks and scale-free networks under fast switching, while in stochastic small-world networks such enhancement is not significant.

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