Robustness of complex networks to global perturbations.

摘要

This thesis studies the robustness of complex dynamical networks with non-trivial topologies against global perturbations, following Robert May's seminal work on network stability, in order to find critical stability thresholds of global perturbations and to determine if their impact varies across different network topologies. Numerical analysis is used as the primary research method. Dynamical networks are randomly generated in the form of a coefficient matrix of stable linear differential equations. The networks are then inflicted with global perturbation (i.e., addition of another random matrix with varying magnitudes) and their stabilities are tested for each perturbation magnitude, to determine at what scale of global perturbation they are jarred to instability.;The results show a monotonic decrease of the instability threshold over increasing link density for all network topologies. For a given link density, random regular networks show highest robustness against global perturbation, closely followed by Watts-Strogatz small-world networks and Erdos-Renyi random graphs, and then Barabasi-Albert scale-free networks are least robust among the four topologies tested. Fully connected networks used in May's original work are found to be consistently unstable in the presence of global perturbation of any magnitude. These findings offer useful implications for the robustness and sustainability/vulnerability of real-world complex networks with nontrivial topologies.