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Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…

Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these…

Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has…

A class of centrality measures called betweenness centralities reflects degree of participation of edges or nodes in communication between different parts of the network. The original shortest-path betweenness centrality is based on…

We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than…

Synchronization processes in populations of locally interacting elements are in the focus of intense research in physical, biological, chemical, technological and social systems. The many efforts devoted to understand synchronization…

In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centrality measures, from which the partial correlation…

We investigate topological and spectral properties of models of European and US-American power grids and of paradigmatic network models as well as their implications for the synchronization dynamics of phase oscillators with heterogeneous…

We study the impact of interaction of nodes in a layer of a multiplex network on the dynamical behavior and cluster synchronization of these nodes in other layers. We find that nodes interactions in one layer affects the cluster…

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial for understanding the function, performance and evolution of complex systems. In the last few…

The production process of integrated electronic circuitry inherently leads to large heterogeneities on the component level. For electronic clock networks this implies detuned intrinsic frequencies and differences in coupling strength and…

The stability (or instability) of synchronization is important in a number of real world systems, including the power grid, the human brain and biological cells. For identical synchronization, the synchronizability of a network, which can…

We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized…

The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally-coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of…

We study a network of coupled logistic maps whose interactions occur with a certain distribution of delay times. The local dynamics is chaotic in the absence of coupling and thus the network is a paradigm of a complex system. There are two…

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…

In temporal networks, where nodes interact via sequences of temporary events, information or resources can only flow through paths that follow the time-ordering of events. Such temporal paths play a crucial role in dynamic processes.…

The question of how network topology influences emergent synchronized oscillations in excitable media is addressed. Coupled van der Pol-FitzHugh-Nagumo elements arranged either on regular rings or on clusters of the square lattice are…

In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…

Synchronization dynamics is a phenomenon of great interest in many fields of science. One of the most important fields is neuron dynamics, as synchronization in certain regions of the brain is related to some of the most common mental…