Sandpile cascades on oscillator networks: The BTW model meets Kuramoto
Abstract
Cascading failures abound in complex systems and the BakTangWeisenfeld (BTW) sandpile model provides a theoretical underpinning for their analysis. Yet, it does not account for the possibility of nodes having oscillatory dynamics, such as in power grids and brain networks. Here, we consider a network of Kuramoto oscillators upon which the BTW model is unfolding, enabling us to study how the feedback between the oscillatory and cascading dynamics can lead to new emergent behaviors. We assume that the more outofsync a node is with its neighbors, the more vulnerable it is and lower its loadcarrying capacity accordingly. Also, when a node topples and sheds load, its oscillatory phase is reset at random. This leads to novel cyclic behavior at an emergent, long timescale. The system spends the bulk of its time in a synchronized state where load builds up with minimal cascades. Yet, eventually, the system reaches a tipping point where a large cascade triggers a "cascade of larger cascades," which can be classified as a dragon king event. The system then undergoes a short transient back to the synchronous, buildup phase. The coupling between capacity and synchronization gives rise to endogenous cascade seeds in addition to the standard exogenous ones, and we show their respective roles. We establish the phenomena from numerical studies and develop the accompanying meanfield theory to locate the tipping point, calculate the load in the system, determine the frequency of the longtime oscillations, and find the distribution of cascade sizes during the buildup phase.
 Publication:

Chaos
 Pub Date:
 May 2022
 DOI:
 10.1063/5.0095094
 arXiv:
 arXiv:2112.00104
 Bibcode:
 2022Chaos..32e3121M
 Keywords:

 Nonlinear Sciences  Adaptation and SelfOrganizing Systems;
 Condensed Matter  Disordered Systems and Neural Networks;
 Mathematics  Dynamical Systems;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 13 pages, 11 figures