Complex networks appear in almost every aspect of our daily life and are widely studied in
the fields of physics, mathematics, finance, biology and computer science. This work utilizes
percolation theory in statistical physics to explore the percolation properties of
complex networks and develops a reinforcement scheme on improving network resilience.
This dissertation covers two major parts of my Ph.D. research on complex networks:
i) probe—in the context of both traditional percolation and k-core percolation—the resilience
of complex networks with tunable degree distributions or directed dependency links under
random, localized or targeted attacks; ii) develop and propose a
reinforcement scheme to eradicate catastrophic collapses that occur very often in interdependent networks.
We first use generating function and probabilistic methods to obtain analytical solutions to
percolation properties of interest, such as the giant component size and the critical occupation probability.
We study uncorrelated random networks with Poisson, bi-Poisson, power-law, and Kronecker-delta degree
distributions and construct those networks which are based on the configuration model.
The computer simulation results show remarkable agreement
with theoretical predictions.
We discover an increase of network robustness as the degree distribution
broadens and a decrease of network robustness as directed dependency links come into play
under random attacks. We also find that targeted attacks exert the biggest damage to
the structure of both single and interdependent networks in k-core percolation.
To strengthen the resilience of interdependent networks, we develop and propose a reinforcement
strategy and obtain the critical amount of reinforced nodes analytically for interdependent
Erdős-Rényi networks and numerically for scale-free and for random regular networks.
Our mechanism leads to improvement of network stability of the West U.S. power grid.
This dissertation provides us with a deeper understanding of the effects of structural features on network
stability and fresher insights into designing resilient interdependent infrastructure networks.
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/27354 |
| Date | 27 January 2018 |
| Creators | Yuan, Xin |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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