Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks

Synchronization is of central importance in power distribution, telecommunication, neuronal, and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand the conditions under which they form, except for in the simplest of networks. In this article, we shed light on the intimate connection between network symmetry and cluster synchronization. We introduce general techniques that use network symmetries to reveal the patterns of synchronized clusters and determine the conditions under which they persist. The connection between symmetry and cluster synchronization is experimentally explored using an electro-optic network. We experimentally observe and theoretically predict a surprising phenomenon in which some clusters lose synchrony while leaving others synchronized. The results could guide the design of new power grid systems or lead to new understanding of the dynamical behavior of networks ranging from neural to social

Comment on ``Intermittent Synchronization in a Pair of Coupled Chaotic Pendula"

The main aim of this comment is to emphasize that the conditional Lyapunov exponents play an important role in distinguishing between intermittent and persistent synchronization, when the analytic criteria for asymptotic stability are not uniformly obeyed.Comment: 2 pages, RevTeX 4, 1 EPS figur

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

Network synchronization: Spectral versus statistical properties

We consider synchronization of weighted networks, possibly with asymmetrical connections. We show that the synchronizability of the networks cannot be directly inferred from their statistical properties. Small local changes in the network structure can sensitively affect the eigenvalues relevant for synchronization, while the gross statistical network properties remain essentially unchanged. Consequently, commonly used statistical properties, including the degree distribution, degree homogeneity, average degree, average distance, degree correlation, and clustering coefficient, can fail to characterize the synchronizability of networks

Studio della correlazione tra il tremore vulcanico e l’attività esplosiva dell’Etna nel Gennaio - Febbraio 1999 mediante il sistema VoTA (Volcanic Tremor Analyzer)

Il seguente lavoro presenta lo studio della correlazione tra il tremore vulcanico e l'attività esplosiva dell'Etna nel gennaio-febbraio 1999 effettuato mediante l’implementazione e lo sviluppo del sistema automatico per l’analisi e la visualizzazione del tremore vulcanico VoTA (Volcanic Tremor Analizer). In particolare, sono stati presi in considerazione cinque episodi eruttivi significativi dell’attività dell’Etna durante i quali il VoTA ha effettuato un’analisi on line del tremore vulcanico. Successivamente, tali dati sono stati confrontati con le immagini dell’attività eruttiva riprese dalla telecamera di sorveglianza dell’Etna, permettendo di ricavare delle correlazioni tra le diverse fasi dell’attività esplosiva ed i corrispondenti valori del tremore vulcanico

Enhancing Synchrony in Chaotic Oscillators by Dynamic Relaying

In a chain of mutually coupled oscillators, the coupling threshold for synchronization between the outermost identical oscillators decreases when a type of impurity (in terms of parameter mismatch) is introduced in the inner oscillator(s). The outer oscillators interact indirectly via dynamic relaying, mediated by the inner oscillator(s). We confirm this enhancing of critical coupling in the chaotic regimes of R\"ossler system in absence of coupling delay and in Mackey-Glass system with delay coupling. The enhancing effect is experimentally verified in electronic circuit of R\"ossler oscillators.Comment: 4 pages, 9 figure

Electronic circuit implementation of chaos synchronization

In this paper, an electronic circuit implementation of a robustly chaotic two-dimensional map is presented. Two such electronic circuits are realized. One of the circuits is configured as the driver and the other circuit is configured as the driven system. Synchronization of chaos between the driver and the driven system is demonstrated