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We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working…
Power grid networks, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted…
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…
When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another…
Due to time delays in signal transmission and processing, phase lags are inevitable in realistic complex oscillator networks. Conventional wisdom is that phase lags are detrimental to network synchronization. Here we show that judiciously…
High levels of penetration of distributed generation and aggressive reactive power compensation with modern power electronics may result in the reversal of active and reactive power flows in future distribution grids. The voltage stability…
The nature of emergent collective behaviors of moving physical agents interacting with their neighborhood is a long-standing open issue in physical and biological systems alike. This calls for studies on the control of synchronization and…
We propose a methodology to analyze synchronization in an ensemble of diffusively coupled multistable systems. First, we study how two bidirectionally coupled multistable oscillators synchronize and demonstrate the high complexity of the…
Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…
This study explores a method to characterize temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the…
Certifying power flow solvability is important for reliable power system operations under volatile operating conditions, but solving power flow equations repeatedly can be costly and may encounter convergence issues. In this paper, we…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
We study the reliability of phase oscillator networks in response to fluctuating inputs. Reliability means that an input elicits essentially identical responses upon repeated presentations, regardless of the network's initial condition. In…
We introduce a model to study the effect of degree-frequency correlations on synchronization in networks of coupled oscillators. Analyzing this model, we find several remarkable characteristics. We find a stationary synchronized state that…
This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different…
We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically…
The electric power system is one of the cornerstones of modern society. One of its most serious malfunctions is the blackout, a catastrophic event that may disrupt a substantial portion of the system, playing havoc to human life and causing…
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 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…
Phase-locked solutions of coupled oscillators are studied with asymmetric coupling strengths or inhomogeneous natural frequencies. The solutions show remarkable profiles of phase lags from the pacemaker corresponding to the ratio of upward…