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

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

Comparability of Functional MRI Response in Young and Old During Inhibition

When using fMRI to study age-related cognitive changes, it is important to establish the integrity of the hemodynamic response because, potentially, it can be affected by age and disease. However, there have been few attempts to document such integrity and no attempts using higher cognitive rather than perceptual or motor tasks. We used fMRI with 28 healthy young and older adults on an inhibitory control task. Although older and young adults differed in task performance and activation patterns, they had comparable hemodynamic responses. We conclude that activation during cognitive inhibition, which was predominantly increased in elders, was not due to vascular confounds or specific changes in hemodynamic coupling

On the coexistence of stellar-mass and intermediate-mass black holes in globular clusters

In this paper, we address the question: What is the probability of stellar-mass black hole (BH) binaries co-existing in a globular cluster with an intermediate-mass black hole (IMBH)? Our results suggest that the detection of one or more BH binaries can strongly constrain the presence of an IMBH in most Galactic globular clusters. More specifically, the detection of one or more BH binaries could strongly indicate against the presence of an IMBH more massive than $\gtrsim 10^3$ M$_{\rm \odot}$ in roughly 80\% of the clusters in our sample. To illustrate this, we use a combination of N-body simulations and analytic methods to weigh the rate of formation of BH binaries against their ejection and/or disruption rate via strong gravitational interactions with the central (most) massive BH. The eventual fate of a sub-population of stellar-mass BHs (with or without binary companions) is for all BHs to be ejected from the cluster by the central IMBH, leaving only the most massive stellar-mass BH behind to form a close binary with the IMBH. During each phase of evolution, we discuss the rate of inspiral of the central BH-BH pair as a function of both the properties of the binary and its host cluster.Comment: 16 pages, 8 figures, 1 table, accepted for publication in MNRA