Localization Phenomena in Networks: Implications for Fragility and Dynamic Response

Localized eigenvectors and eigenfunctions are those which have most of their mass in a very small region. When these are the eigenvectors of the Laplacian of 2nd-order oscillator networks, this localization phenomenon has significant implications to robustness/fragility with unmodeled dynamics.

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Example of a network where some eigenvectors as Localized

Implications for robustness (visualized using pseudospectra)