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We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…
Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean…
Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On…
The problem of synchronization of coupled self-oscillators by external force is studied. The charts of Lyapunov's exponents in the "frequency - amplitude" parameter plane are obtained within the framework of the phase approximation. We…
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize…
We examine microscopic mechanisms for coupling stochastic oscillators so that they display similar and correlated temporal variations. Unlike oscillatory motion in deterministic dynamical systems, complete synchronization of stochastic…
Community structure can naturally emerge in paths to synchronization, and scratching it from the paths is a tough issue that accounts for the diverse dynamics of synchronization. In this paper, with assumption that the synchronization on…
To observe synchronization in a large network of classical or quantum systems demands both excellent control of the interactions between the nodes and very accurate preparation of the initial conditions due to the involved nonlinearities…
We investigate a generalized Kuramoto phase-oscillator model with Hebb-like couplings that evolve according to a stochastic differential equation on various topologies. Numerical simulations show that even with identical oscillators, there…
We analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random…
We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and…
We study populations of oscillators, all-to-all coupled by means of quenched disordered phase shifts. While there is no traditional synchronization transition with a nonvanishing Kuramoto order parameter, the system demonstrates a specific…
We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of…
The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized…
Synchronization is an ubiquitous phenomenon in dynamical systems of networked oscillators. While it is often a goal to achieve, in some context one would like to decrease it, e.g., although synchronization is essential to the good…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
In this paper, we propose an $N$ oscillators Kuramoto model with quaternions $\mathbb{H}$. In case the coupling strength is strong, a sufficient condition of synchronization is established for general $N\geqslant 2$. On the other hand, we…