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Résumé |
A theoretical framework for studying percolation of interdependent networks will be presented. In
interdependent networks, such as
infrastructures, when nodes in one network fail, they cause dependent nodes in other networks to also fail.
This may happen recursively
and can lead to a cascade of failures and to a sudden fragmentation of the system. This is in contrast to a
single network where the
percolation transition due to failures is continuous. I will present analytical solutions based on percolation
theory, for the critical
thresholds, cascading failures, and the giant functional component of a network of n interdependent
networks. Our analytical results
show that a single network studied for 80 years is just a limited case, n=1, of the general and a significantly
richer case of n>1. I will also
show that interdependent networks embedded in space are significantly more vulnerable and have richer
behavior compared to non-
embedded networks. In particular, small localized attacks of zero fraction but above a critical size lead to
cascading failures that
dynamically propagate like nucleation and yield an abrupt phase transition. I will finally show that the
abstract interdependent
percolation theory and its novel behavior in networks of networks can be realized and proved in controlled
experiments in real physical
systems. I will discuss the consequences of the recent theory of interdependent networks on phase
transitions in real physical
iinterdependent systems and present theory and experiments on interdependent superconducting networks
where we recently identified
a novel abrupt transition although each isolated system shows a continuous transition.
References:
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[3] A. Bashan et al, Nature Physics, 9, 667 (2013)
[4] A Majdandzic et al, Nature Physics 10 (1), 34 (2014); Nature Comm. 7, 10850 (2016)
[5] M. Danziger et al, Nature Physics 15(2), 178 (2019)
[6] B. Gross, I Bonamassa and S. Havlin, Fractal fluctuations at mixed-order transitions in interdependent
networks, 129 (26), 268301
(2022)
[7] I Bonamassa, Interdependent superconducting networks, preprint arXiv:2207.01669 (2022), Nature
Physics (in press, 2023) |
