Related papers: Modelling power grids as pseudo adaptive networks
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's…
We investigate the role of inertia in the asynchronous state of a disordered Kuramoto model. We extend an iterative simulation scheme to the case of the Kuramoto model with inertia in order to determine the self-consistent fluctuation…
We present two different approaches to model power grids as interconnected networks of networks. Both models are derived from a model for spatially embedded mono-layer networks and are generalised to handle an arbitrary number of network…
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…
Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of many nodes, the resulting dynamics are typically…
The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate…
We study two intertwined globally coupled networks of noisy Kuramoto phase oscillators that have the same natural frequency, but differ in their perception of the mean field and their contribution to it. Such a give-and-take mechanism is…
We study a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity in interaction. Under a week force, an oscillator tends to follow the…
We propose a concept to generate and stabilize diverse partial synchronization patterns (phase clusters) in adaptive networks which are widespread in neuro- and social sciences, as well as biology, engineering, and other disciplines. We…
We study synchronization of Kuramoto oscillators in strongly modular networks in which the structure of the network inside each community is averaged. We find that the dynamics of the interacting communities can be described as an ensemble…
Power grids must modernize to meet climate goals while maintaining reliable and stable operating conditions. Yet progress is hindered by a limited understanding of the stochastic processes underlying grid frequency and phase-angle…
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…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscilla- tors with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for…
While phase oscillators are often used to model neuronal populations, in contrast to the Kuramoto paradigm, strong interactions between brain areas can be associated with loss of synchrony. Using networks of coupled oscillators described by…
This paper studies the celebrated Kuramoto-Sakaguchi model of coupled oscillators adopting two recent concepts. First, we consider appropriately-defined subsets of the $n$-torus called winding cells. Second, we analyze the semicontractivity…
Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
We propose a synthetical weights' dynamic mechanism for weighted networks which takes into account the influences of strengths of nodes, weights of links and incoming new vertices. Strength/Weight preferential strategies are used in these…