Fluctuation-induced distributed resonances in oscillatory networks

Abstract

Across physics, biology, and engineering, the collective dynamics of oscillatory networks often evolve into self-organized operating states. How such networks respond to external fluctuating signals fundamentally underlies their function, yet is not well understood. Here, we present a theory of dynamic network response patterns and reveal how distributed resonance patterns emerge in oscillatory networks once the dynamics of the oscillatory units become more than one-dimensional. The network resonances are topology specific and emerge at an intermediate frequency content of the input signals, between global yet homogeneous responses at low frequencies and localized responses at high frequencies. Our analysis reveals why these patterns arise and where in the network they are most prominent. These results may thus provide general theoretical insights into how fluctuating signals induce response patterns in networked systems and simultaneously help to develop practical guiding principles for real-world network design and control.

Open data base analysis of scaling and spatio-temporal properties of power grid frequencies

“…Our results on the spatial dependencies in the Continental European (CE) synchronous area are also highly relevant for the operation of power grids and other research in the field. The observations that the long term behaviour is almost identical throughout the synchronous area but short time fluctuations differ, are in agreement with earlier theoretical findings [21]. Based on the DFA results ( Figs.…”

“…There will only be few independent paths available for weakly coupled locations such as Istanbul, potentially explaining the large "time to bulk". Clearly, further research is necessary to validate and adjust spatio-temporal models of the power grid in light of these new data [21].…”

“…Analysis and modelling of the power grid frequency and its statistics and complex dynamics have become * b.schaefer@qmul.ac.uk increasingly popular in the interdisciplinary community, attracting also much attention from mathematicians and physicists. Studies have investigated for example different dynamical models [13][14][15], compared centralised vs. decentralised topologies [16][17][18], investigated the effect of fluctuations on the grid's stability [19,20], or how fluctuations propagate [21,22]. Further research proposed real-time pricing schemes [23], optimised the placement of (virtual) inertia [24,25], or investigated cascading failures in power grids [26][27][28][29].…”

Stochastic properties of the frequency dynamics in real and synthetic power grids

“…Typically, the frequency at each node is very close to the bulk frequency throughout the grid, with fluctuations indicating the gross power balance. Notable exceptions are high-frequency disturbances, which are typically localised [43,44], or inter-area oscillations, where energy is oscillating from one part of the grid to another one. The synthetic model of the frequency dynamics is discussed in detail in [14].…”

Time delay effects in the control of synchronous electricity grids

“…The linearized system has been extensively studied in the analysis of power system stability 6,8 , transient dynamics and propagation of disturbances in power grids 30,36,37 . Note that the stationary power input P i,0 is missing in Eq.…”