Related papers: Taming Cluster Synchronization
This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly…
Synchronisation and pattern formation have been intensely addressed for systems evolving on static networks. Extending the study to include the inherent ability of the network to adjust over time proved cumbersome and led to conclusions…
We study cluster synchronization of networks and propose a canonical transformation for simultaneous block diagonalization of matrices that we use to analyze stability of the cluster synchronous solution. Our approach has several advantages…
Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix…
A method for engineering the behavior of populations of rhythmic elements is presented. The framework, which is based on phase models, allows a nonlinear time-delayed global feedback signal to be constructed which produces an interaction…
Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…
Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics…
Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix. Simple methods are proposed to generate a (separate) linear coupling gain…
A novel regime of synchronization, called remote synchronization, where the peripheral nodes form a phase synchronized cluster not including the hub, was recently observed in star motifs. We show the existence of a more general dynamical…
Using a recently described technique for manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson…
Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by…
In large groups, every collaborative act requires balancing two pressures: the need to achieve behavioural synchrony and the need to keep free riding to a minimum. This paper introduces a model of collaboration that requires both…
Spectral clustering is a popular and effective algorithm designed to find $k$ clusters in a graph $G$. In the classical spectral clustering algorithm, the vertices of $G$ are embedded into $\mathbb{R}^k$ using $k$ eigenvectors of the graph…
Small networks of chaotic units which are coupled by their time-delayed variables, are investigated. In spite of the time delay, the units can synchronize isochronally, i.e. without time shift. Moreover, networks can not only synchronize…
Although the set of permutation symmetries of a complex network can be very large, few of the symmetries give rise to stable synchronous patterns. Here we present a new framework and develop techniques for controlling synchronization…
Algorithms for the synchronisation of clocks across networks are both common and important within distributed systems. We here address not only the formal modelling of these algorithms, but also the formal verification of their behaviour.…
We investigate the emergence of synchronization in heterogeneous networks of chaotic maps. Our findings reveal that a small cluster of highly connected maps is responsible for triggering the spark of synchronization. After the spark, the…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
We study collective synchronization of pulse-coupled oscillators interacting on asymmetric random networks. We demonstrate that random matrix theory can be used to accurately predict the speed of synchronization in such networks in…
Unsupervised clustering, also known as natural clustering, stands for the classification of data according to their similarities. Here we study this problem from the perspective of complex networks. Mapping the description of data…