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We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors…
Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for…
Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world…
The paper is concerned with the interplay between network structure and traffic dynamics in a communications network, from the viewpoint of end-to-end performance of packet transfer. We use a model of network generation that allows the…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
The structure and dynamic of social network are largely determined by the heterogeneous interaction activity and social capital allocation of individuals. These features interplay in a non-trivial way in the formation of network and…
Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…
Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to…
We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. A striking feature of these networks is that they are chaotic. How does this chaos manifest in the neural code? Specifically, how variable are…
We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to…
This paper investigates the frequency control of multi-machine power systems subject to uncertain and dynamic net loads. We propose distributed internal model controllers that coordinate synchronous generators and demand response to tackle…
The effects of demographic stochasticity in the long term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour…
Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…
In both natural and engineered systems, communication often occurs dynamically over networks ranging from highly structured grids to largely disordered graphs. To use, or comprehend the use of, networks as efficient communication media…
We give a complete characterization of the possible response matrices at a fixed frequency of n-terminal electrical networks of inductors, capacitors, resistors and grounds, and of n-terminal discrete linear elastodynamic networks of…