- Titel
- Fluctuation response patterns of network dynamics - An introduction
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-899978
- Quellenangabe
- European journal of applied mathematics
Erscheinungsjahr: 2023
Jahrgang: 34
Seiten: 429-466
E-ISSN: 1469-4425 - Erstveröffentlichung
- 2022
- Abstract (EN)
- Networked dynamical systems, i.e., systems of dynamical units coupled via nontrivial interaction topologies, constitute models of broad classes of complex systems, ranging from gene regulatory and metabolic circuits in our cells to pandemics spreading across continents. Most of such systems are driven by irregular and distributed fluctuating input signals from the environment. Yet how networked dynamical systems collectively respond to such fluctuations depends on the location and type of driving signal, the interaction topology and several other factors and remains largely unknown to date. As a key example, modern electric power grids are undergoing a rapid and systematic transformation towards more sustainable systems, signified by high penetrations of renewable energy sources. These in turn introduce significant fluctuations in power input and thereby pose immediate challenges to the stable operation of power grid systems. How power grid systems dynamically respond to fluctuating power feed-in as well as other temporal changes is critical for ensuring a reliable operation of power grids yet not well understood. In this work, we systematically introduce a linear response theory (LRT) for fluctuation-driven networked dynamical systems. The derivations presented not only provide approximate analytical descriptions of the dynamical responses of networks, but more importantly, also allow to extract key qualitative features about spatio-temporally distributed response patterns. Specifically, we provide a general formulation of a LRT for perturbed networked dynamical systems, explicate how dynamic network response patterns arise from the solution of the linearised response dynamics, and emphasise the role of LRT in predicting and comprehending power grid responses on different temporal and spatial scales and to various types of disturbances. Understanding such patterns from a general, mathematical perspective enables to estimate network responses quickly and intuitively, and to develop guiding principles for, e.g., power grid operation, control and design.
- Andere Ausgabe
- Link zum Artikel der zuerst in der Zeitschrift „European journal of applied mathematics” bei Cambridge University Press erschienen ist.
DOI: 10.1017/S0956792522000201 - Freie Schlagwörter (DE)
- Vernetzte dynamische Systeme, lineare Antworttheorie, Fluktuationen, dynamische Antworten, Musterbildung, Störungsausbreitung, oszillierende Netzwerke, Stromnetzdynamik
- Freie Schlagwörter (EN)
- Networked dynamical systems, linear response theory, fluctuations, dynamic responses, pattern formation, perturbation spreading, oscillatory networks, power grid dynamics
- Klassifikation (DDC)
- 510
- Verlag
- Cambridge Univ. Press, Cambridge
- Förder- / Projektangaben
- Deutsche Forschungsgemeinschaft (DFG)
Excellence Strategy
(XC-2068)
ID: 390729961 - National Natural Science Foundation of China ID: 12161141016
- Shanghai Municipal Science and Technology Major Project Major Project
ID: 2021SHZDZX0100 - Shanghai Municipal Commission of Science and Technology Project ID: 18ZR1442000 and 19511132101
- German Federal Ministry for Research and Education (BMBF)
ID: 03SF0472F and 03EK3055F - Version / Begutachtungsstatus
- publizierte Version / Verlagsversion
- URN Qucosa
- urn:nbn:de:bsz:14-qucosa2-899978
- Veröffentlichungsdatum Qucosa
- 01.03.2024
- Dokumenttyp
- Artikel
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
CC BY-SA 4.0