Related papers: Modelling power grids as pseudo adaptive networks
Networks of coupled phase oscillators play an important role in the analysis of emergent collective phenomena. In this article, we introduce generalized $m$-splay states constituting a special subclass of phase-locked states with vanishing…
We study the synchronization of oscillators with inertias and phase shifts, namely the second-order Kuramoto-Sakaguchi model. Using the self-consistent method, we find that the effect of inertia is the introduction of effective phase…
We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic,…
Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes' recovery to phase…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
Robust coordination and organization in large ensembles of nonlinear oscillatory units play a vital role in a wide range of natural and engineered system. The control of self-organizing network-coupled systems has recently seen significant…
With the increasing inclusion of regenerative resources in the energy mix, their intermittent character challenges power grid stability. Hence it is essential to determine which input fluctuations power grids are particularly vulnerable to.…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A coupled oscillator network is characterized by a population of heterogeneous oscillators and a graph describing…
This paper proposes a novel second order mathematical model in the Kuramoto framework to simulate and study low frequency oscillations in power systems. This model facilitates better understanding of the complex dynamics of a power network.…
Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and becomes incoherent with the rest of the network. Such chimera-type patterns with an incoherent state formed by a single…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
We investigate states of enhanced activity in a biological neuronal network composed of pulse-coupled oscillators. The synaptic couplings between the neurons are dynamic, modeling spike time dependent plasticity. The network exhibits…
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…
In view of highly decentralized and diversified power generation concepts, in particular with renewable energies such as wind and solar power, the analysis and control of the stability and the synchronization of power networks is an…
Understanding the sensitivity of a system's behavior with respect to parameter changes is essential for many applications. This sensitivity may be desired - for instance in the brain, where a large repertoire of different dynamics,…
80% of all Renewable Energy Power in Germany is installed in tree-like distribution grids. Intermittent power fluctuations from such sources introduce new dynamics into the lower grid layers. At the same time, distributed resources will…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
We investigate the role of connection density in an adaptive network model of chaotic units that dynamically rewire based on their internal states and local coherence. By systematically varying the network's connectivity density, we uncover…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…