Related papers: Complete Characterization of Stability of Cluster …
Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…
Swarming phenomena are ubiquitous in various physical, biological, and social systems, where simple local interactions between individual units lead to complex global patterns. A common feature of diverse swarming phenomena is that the…
This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of…
Identifying key players in a set of coupled individual systems is a fundamental problem in network theory. Its origin can be traced back to social sciences and led to ranking algorithms based on graph theoretic centralities. Coupled…
Dynamical properties of complex networks are related to the spectral properties of the Laplacian matrix that describes the pattern of connectivity of the network. In particular we compute the synchronization time for different types of…
The interaction topology among the constituents of a complex network plays a crucial role in the network's evolutionary mechanisms and functional behaviors. However, some network topologies are usually unknown or uncertain. Meanwhile,…
Synchronization, that occurs both for non-chaotic and chaotic systems, is a striking phenomenon with many practical implications in natural phenomena. However, even before synchronization, strong correlations occur in the collective…
We study networks with linear dynamics where the presence of symmetries of the pair (A,B) induces a partition of the network nodes in clusters and the matrix A is not restricted to be in Laplacian form. For these networks, an invariant…
Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative…
Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units.…
Cluster synchronization is of great importance for the normal functioning of numerous technological and natural systems. Deviations from normal cluster synchronization patterns are closely associated with various malfunctions, such as…
In the past few years, the discoveries of small-world and scale-free properties of many natural and artificial complex networks have stimulated significant advances in better understanding the relationship between the topology and the…
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…
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…
The stability analysis of synchronization in time-varying higher-order networked structures (simplicial complexes) is one of the challenging problem due to the presence of time-varying group interactions. In this context, most of the…
For spiking neural networks we consider the stability problem of global synchrony, arguably the simplest non-trivial collective dynamics in such networks. We find that even this simplest dynamical problem -- local stability of synchrony --…
In this paper, the fixed-time cluster synchronization problem for complex networks via pinning control is discussed. Fixed-time synchronization has been a hot topic in recent years, which means that the network can achieve synchronization…
A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes…
Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…
In this work we study the dynamics of Kuramoto oscillators on a stochastically evolving network whose evolution is governed by the phases of the individual oscillators and degree distribution. Synchronization is achieved after a threshold…