Hierarchical synchronization in complex networks with heterogeneous degrees.
@article{Zhou2006HierarchicalSI,
title={Hierarchical synchronization in complex networks with heterogeneous degrees.},
author={Changsong Zhou and J{\"u}rgen Kurths},
journal={Chaos},
year={2006},
volume={16 1},
pages={
015104
}
}We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are…
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References
SHOWING 1-10 OF 94 REFERENCES
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.
Synchronization on small-world networks.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002
Phase synchronization is observed to emerge in the presence of even a tiny fraction P of shortcuts and to display saturated behavior for P > or similar to 0.5, indicating that the same synchronizability as the random network (P=1) can be achieved with relatively small number of shortcuts.
Network synchronization, diffusion, and the paradox of heterogeneity.
- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005
This analysis reveals a striking relation between this process and the condition for the linear stability of the synchronized states and shows that, for a given degree distribution, the maximum synchronizability is achieved when the network of coupling is weighted and directed and the overall cost involved in the couplings is minimum.
Frequency clustering of coupled phase oscillators on small-world networks
- Physics
- 2005
Abstract.We analyze the phenomenon of frequency clustering in a system of
coupled phase oscillators. The oscillators, which in the absence
of coupling have uniformly distributed natural frequencies,…
Breaking synchrony by heterogeneity in complex networks.
- Computer SciencePhysical review letters
- 2004
For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global…
Enhancing complex-network synchronization
- Physics
- 2005
Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted…
Random coupling of chaotic maps leads to spatiotemporal synchronization.
- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002
The spatiotemporal dynamics of a network of coupled chaotic maps, with varying degrees of randomness in coupling connections, are investigated and the regularizing effect of random connections can be understood from stability analysis of the probabilistic evolution equation for the system.
Heterogeneity in oscillator networks: are smaller worlds easier to synchronize?
- Computer SciencePhysical review letters
- 2003
It is found that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger.