104,143 research outputs found
Synchronization processes in complex networks
We present an extended analysis, based on the dynamics towards
synchronization of a system of coupled oscillators, of the hierarchy of
communities in complex networks. In the synchronization process, different
structures corresponding to well defined communities of nodes appear in a
hierarchical way. The analysis also provides a useful connection between
synchronization dynamics, complex networks topology and spectral graph
analysis.Comment: 16 pages, 4 figures. To appear in Physica D "Special Issue on
dynamics on complex networks
Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks
We study projective-anticipating, projective, and projective-lag
synchronization of time-delayed chaotic systems on random networks. We relax
some limitations of previous work, where projective-anticipating and
projective-lag synchronization can be achieved only on two coupled chaotic
systems. In this paper, we can realize projective-anticipating and
projective-lag synchronization on complex dynamical networks composed by a
large number of interconnected components. At the same time, although previous
work studied projective synchronization on complex dynamical networks, the
dynamics of the nodes are coupled partially linear chaotic systems. In this
paper, the dynamics of the nodes of the complex networks are time-delayed
chaotic systems without the limitation of the partial-linearity. Based on the
Lyapunov stability theory, we suggest a generic method to achieve the
projective-anticipating, projective, and projective-lag synchronization of
time-delayed chaotic systems on random dynamical networks and find both the
existence and sufficient stability conditions. The validity of the proposed
method is demonstrated and verified by examining specific examples using Ikeda
and Mackey-Glass systems on Erdos-Renyi networks.Comment: 14 pages, 6 figure
Synchronizability determined by coupling strengths and topology on Complex Networks
We investigate in depth the synchronization of coupled oscillators on top of
complex networks with different degrees of heterogeneity within the context of
the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)],
we unveiled how for fixed coupling strengths local patterns of synchronization
emerge differently in homogeneous and heterogeneous complex networks. Here, we
provide more evidence on this phenomenon extending the previous work to
networks that interpolate between homogeneous and heterogeneous topologies. We
also present new details on the path towards synchronization for the evolution
of clustering in the synchronized patterns. Finally, we investigate the
synchronization of networks with modular structure and conclude 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. The present work introduces new parameters that
are proved to be useful for the characterization of synchronization phenomena
in complex networks.Comment: 11 pages, 10 figures and 1 table. APS forma
Synchronization reveals topological scales in complex networks
We study the relationship between topological scales and dynamic time scales
in complex networks. The analysis is based on the full dynamics towards
synchronization of a system of coupled oscillators. In the synchronization
process, modular structures corresponding to well defined communities of nodes
emerge in different time scales, ordered in a hierarchical way. The analysis
also provides a useful connection between synchronization dynamics, complex
networks topology and spectral graph analysis.Comment: 4 pages, 3 figure
Synchronization and modularity in complex networks
We investigate the connection between the dynamics of synchronization and the
modularity on complex networks. Simulating the Kuramoto's model in complex
networks we determine patterns of meta-stability and calculate the modularity
of the partition these patterns provide. The results indicate that the more
stable the patterns are, the larger tends to be the modularity of the partition
defined by them. This correlation works pretty well in homogeneous networks
(all nodes have similar connectivity) but fails when networks contain hubs,
mainly because the modularity is never improved where isolated nodes appear,
whereas in the synchronization process the characteristic of hubs is to have a
large stability when forming its own community.Comment: To appear in the Proceedings of Workshop on Complex Systems: New
Trends and Expectations, Santander, Spain, 5-9 June 200
Complete Characterization of Stability of Cluster Synchronization in Complex Dynamical Networks
Synchronization is an important and prevalent phenomenon in natural and
engineered systems. In many dynamical networks, the coupling is balanced or
adjusted in order to admit global synchronization, a condition called Laplacian
coupling. Many networks exhibit incomplete synchronization, where two or more
clusters of synchronization persist, and computational group theory has
recently proved to be valuable in discovering these cluster states based upon
the topology of the network. In the important case of Laplacian coupling,
additional synchronization patterns can exist that would not be predicted from
the group theory analysis alone. The understanding of how and when clusters
form, merge, and persist is essential for understanding collective dynamics,
synchronization, and failure mechanisms of complex networks such as electric
power grids, distributed control networks, and autonomous swarming vehicles. We
describe here a method to find and analyze all of the possible cluster
synchronization patterns in a Laplacian-coupled network, by applying methods of
computational group theory to dynamically-equivalent networks. We present a
general technique to evaluate the stability of each of the dynamically valid
cluster synchronization patterns. Our results are validated in an electro-optic
experiment on a 5 node network that confirms the synchronization patterns
predicted by the theory.Comment: 6 figure
- …