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Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the transient…
Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a…
Synchronization in power systems is traditionally achieved through physical network coupling, whereby inverter-based resources (IBRs) and synchronous machines converge to a common frequency via oscillatory swing dynamics. In conventional…
Synchronization is ubiquitous in nature, which is mathematically described by coupled oscillators. Synchronization strongly depends on the interaction network, and the network plays a crucial role in controlling the dynamics. To understand…
We are flooded with large-scale dynamic networked data. Analyses requiring exact comparisons between networks are computationally intractable, so new methodologies are sought. We extend the graphlet-based statistics to directed networks and…
We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the…
We follow up on the study of correlations between GDP's of rich countries. We analyze web-downloaded data on GDP that we use as individual wealth signatures of the country economical state. We calculate the yearly fluctuations of the GDP.…
Understanding the structure and formation of networks is a central topic in complexity science. Economic networks are formed by decisions of individual agents and thus not properly described by established random graph models. In this…
This paper gives a fresh look at network synchronization. Here we no longer analyze it from the view of mathematics, such as graph theory, while we probe into one from control theory. First, we analyze the synchronization region using the…
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…
In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…
In economic and financial networks, the strength of each node has always an important economic meaning, such as the size of supply and demand, import and export, or financial exposure. Constructing null models of networks matching the…
Many natural and engineered complex networks have intricate mesoscopic organization, e.g., the clustering of the constituent nodes into several communities or modules. Often, such modularity is manifested at several different hierarchical…
Using the new data from the OECD-WTO world network of economic activities we construct the Google matrix $G$ of this directed network and perform its detailed analysis. The network contains 58 countries and 37 activity sectors for years…
We study patterns of partial synchronization in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in human subjects. We report the spontaneous occurrence of synchronization phenomena that closely…
An economic system is an exemplar of a complex system in which all agents interact simultaneously. Interactions between countries have generally been studied using the flow of resources across diverse trade networks, in which the degree of…
In this thesis we study synchronization phenomena in natural and artificial coupled multi-component systems, applicable to the scalability of parallel discrete-event simulation for systems with asynchronous dynamics. We analyze the…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…