Spectrum optimization of dynamic networks for reduction of vulnerability against adversarial resonance attacks

Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper, we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant frequency by an adversarial agent with the aim of saturating the network with the signal. Toward this goal, we develop the notion of network vulnerability , which is measured by the expected resonance amplitude on the network under a stochastically modeled adversarial attack. Assuming a second order dynamics model based on the network graph Laplacian and a known stochastic model for the adversarial attack, we propose two methods for minimizing the network vulnerability–one through direct optimization of the spectrum of the network graph, and another through optimization of an auxiliary network graph attached to the main network. We provide theoretical foundations for these methods as well as extensive numerical results analyzing the effectiveness of both methods in reducing the network vulnerability.