# Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators

@article{Papadopoulos2017DevelopmentOS, title={Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators}, author={Lia Papadopoulos and Jason Z. Kim and J{\"u}rgen Kurths and Danielle S. Bassett}, journal={Chaos}, year={2017}, volume={27} }

Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior, and it is interesting to ask how the structural organization of network interactions influences this process. Several studies have explored and uncovered optimal topologies for synchronization by making purposeful alterations to a network. On the other hand, the connectivity patterns of many natural systems are often not static, but are rather modulated over time…

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## 36 Citations

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## References

SHOWING 1-10 OF 123 REFERENCES

Assortative and modular networks are shaped by adaptive synchronization processes.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2012

This work considers a network of interacting phase oscillators, and an adaptation mechanism for the coupling that promotes the connection strengths between those elements that are dynamically correlated, and proves that such an emergent structure is associated with an asymptotic arrangement of the collective dynamical state of the network into cluster synchronization.

On the topology of synchrony optimized networks of a Kuramoto-model with non-identical oscillators.

- Computer ScienceChaos
- 2011

It is demonstrated that synchrony optimized networks can be generated much more cost efficiently by minimization of an energy-like quantity E and subsequent random rewires to control the average path length, and are characterized by a balance between two opposing structural properties.

Emergence of structural patterns out of synchronization in networks with competitive interactions

- Computer ScienceScientific reports
- 2011

The competition between these two adaptive principles leads to the emergence of key structural properties observed in real world networks, such as modular and scale–free structures, together with a striking enhancement of local synchronization in systems with no global order.

Enhancing Synchronization in Systems of Non-identical Kuramoto Oscillators

- Computer ScienceComplex
- 2009

The question whether a a globally synchronized system can be generated by rewirings that improve the local synchronizability is analyzed, and network characteristics and correlations between the oscillator placement on the nodes of the network are discussed.

Synchronization, diversity, and topology of networks of integrate and fire oscillators

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

The analysis shows that regular lattices perform better than a disordered network and this fact can be understood by considering the variability in the number of links between two adjacent neighbors.

Synchronizability determined by coupling strengths and topology on complex networks.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

The present work investigates the synchronization of networks with modular structure and concludes that, in these cases, local synchronization is first attained at the most internal level of organization of modules, progressively evolving to the outer levels as the coupling constant is increased.

Synchronization versus neighborhood similarity in complex networks of nonidentical oscillators.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

The numerical simulations show that the more homogeneous a network, the higher tend to be both the coupling strength required for phase locking and the associated final phase configuration spread over the circle, which means the initial spread of partial synchronization occurs faster for Similar patterns in comparison to Dissimilar ones, while neutral patterns are an intermediate situation between both extremes.

Self-organized network of phase oscillators coupled by activity-dependent interactions.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

We investigate a network of coupled phase oscillators whose interactions evolve dynamically depending on the relative phases between the oscillators. We found that this coevolving dynamical system…