THESIS
2020
Abstract
Various kinds of
fluctuations can occur in different natural or artificial networks and it
can easily endanger the stability of the system. In this thesis, we investigate ways of
enhancing network stability against
fluctuations in the network
flow model and the Kuramoto
model. For the network
flow model, we introduce the message passing algorithm
and discrete Green's function to elucidate how resource
fluctuations determine
flow
fluctuations
in a network optimizing a global cost function. To strengthen the robustness of
the network against
fluctuations, we develop the schemes of optimal bandwidth allocation
in links and optimal resource adjustment in nodes. The changes of loads and currents
prescribed by the optimal bandwidth allocation and resource adjustment sc...[
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Various kinds of
fluctuations can occur in different natural or artificial networks and it
can easily endanger the stability of the system. In this thesis, we investigate ways of
enhancing network stability against
fluctuations in the network
flow model and the Kuramoto
model. For the network
flow model, we introduce the message passing algorithm
and discrete Green's function to elucidate how resource
fluctuations determine
flow
fluctuations
in a network optimizing a global cost function. To strengthen the robustness of
the network against
fluctuations, we develop the schemes of optimal bandwidth allocation
in links and optimal resource adjustment in nodes. The changes of loads and currents
prescribed by the optimal bandwidth allocation and resource adjustment schemes are correlated
with each other, except for some nodes that exhibit relay effects. To examine the
synchronization stability in the network, we study the linear stability of the Kuramoto
model using state dependent algebraic connectivity. Similarly, we propose an optimal
resource adjustment scheme to improve the stability against probabilistic uncertainties of
the natural frequencies. In addition, we introduce a vulnerability measure of individual
nodes to discuss how the topology of the network affects the synchronization stability.
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