Adversarial control of synchronization in complex oscillator networks

TL;DR

The paper addresses the challenge of controlling synchronization in complex oscillator networks. It introduces a gradient-based adversarial perturbation framework that perturbs oscillator phases by small amounts to either enhance or suppress global synchronization, quantified by the order parameter $R$. The main findings show that extremely small perturbations can substantially alter synchronization transitions across diverse topologies, with enhanced synchronization robust to network size and suppression becoming more effective in larger networks, including real-world networks like power grids and brain connectivity. This approach offers a novel, distributed control paradigm that leverages adversarial-inspired perturbations to manage synchronization with minimal intervention, carrying potential implications for infrastructure stability and therapeutic brain modulation.

Abstract

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 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.

Figures (4)

• Figure 1: Synchronization transitions under adversarial perturbations. Order parameter $R$ versus coupling strength $K$ for (a) Erdős–Rényi (ER), (b) Barabási--Albert (BA), and (c) Watts--Strogatz (WS) networks with different perturbation parameters $\epsilon$. Positive $\epsilon$ (red) promotes synchronization, negative $\epsilon$ (blue) suppresses it. Intervention interval $\tau = 0.3$.
• Figure 2: Order parameter $R$ as a function of perturbation strength $|\epsilon|$ for (left to right) Erdős--Rényi (ER), Barabási--Albert (BA), and Watts--Strogatz (WS) networks. Upper panels: enhancement from $R \approx 0.2$ ($K = 0.2$, 0.3, 0.85 for ER, BA, WS respectively); lower panels: suppression from $R \approx 0.8$ ($K = 0.55$, 0.6, 6.0). Filled symbols indicate adversarial attack intervention intervals for a: $\bullet$ ($\tau = 0.1$), $\blacksquare$ ($\tau = 0.3$), $\blacktriangle$ ($\tau = 0.5$), $\blacktriangledown$ ($\tau = 0.7$), and hexagons ($\tau = 1.0$). Crosses shows random perturbation controls for $\tau = 0.1$.
• Figure 3: Order parameter $R$ as a function of network size $N$ for (left to right) Erdős--Rényi (ER), Barabási--Albert (BA), and Watts--Strogatz (WS) networks. Intervention interval $\tau = 0.3$. Upper panels: enhancement from $R \approx 0.2$ ($K = 0.2$, 0.3, 0.85 for ER, BA, WS respectively); lower panels: suppression from $R \approx 0.8$ ($K = 0.55$, 0.6, 6.0). Filled symbols indicate different perturbation parameters $\epsilon$. Crosses show random perturbation controls.
• Figure 4: Order parameter $R$ versus coupling strength $K$ for (a) power network ($N=1138$ and $\langle k \rangle=2.6$) and (b) brain network ($N=987$ and $\langle k \rangle=3.1$) with different perturbation parameters $\epsilon$. Positive $\epsilon$ (red) promotes synchronization, negative $\epsilon$ (blue) suppresses it. Intervention interval $\tau = 0.3$.