Complex network resilience against perturbations

Details

Supervisors

Bianchin, Gianluca ; Delvenne, Jean-Charles

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

enResilience measures how well a system maintains its function under disturbances. In dynamic networks modeled as graphs, whose nodes represent system components and edges represent interactions, recent approaches quantify resilience by finding the smallest single-edge perturbation that moves system poles outside a nominal stability region. This thesis extends this framework to multi-edge disruptive perturbations, focusing on the two-edge case and generalizing to k-edge scenarios. We derive feasibility conditions, analyze convexity under L1- and L2-norm objectives, and design algorithms to compute minimal-cost perturbations. Results show that the use of the L2-norm consistently produces lower costs than the L1-norm, with multi-edge perturbations often providing substantial savings. Applications to a three-species competitive model and a multi-regional epidemic model demonstrate the framework’s ability to shift equilibria toward desired states, such as eliminating invasive species or achieving disease-free conditions. This work advances resilience quantification in complex networks and highlights promising directions for optimizing intervention strategies, such as identifying the minimal combination of changes to network connections needed to eliminate disease spread or restore ecosystem balance.