Adversarial control of synchronization in complex oscillator networks.

This study investigates perturbation strategies inspired by adversarial attack principles from deep learning, designed to control synchronization dynamics through strategically crafted weak perturbations. We propose a gradient-based optimization method that identifies small phase perturbations to dramatically enhance or suppress collective synchronization in Kuramoto oscillator networks. Our approach formulates synchronization control as an optimization problem, computing gradients of the order parameter with respect to oscillator phases to determine optimal perturbation directions. Results demonstrate that extremely small phase perturbations applied to network oscillators can achieve significant synchronization control across diverse network architectures. Our analysis reveals that synchronization enhancement is achievable across various network sizes, while synchronization suppression becomes particularly effective in larger networks, with effectiveness scaling favorably with the network size. The method is systematically validated on canonical model networks including scale-free and small-world topologies and real-world networks representing power grids and brain connectivity patterns. This adversarial framework represents a novel paradigm for synchronization management by introducing deep learning concepts to networked dynamical systems.