Spectral Gradient Iterative Edge Attack for Synchronization Suppression in Complex Networks

Abstract

The synchronization of complex networks, governed by the generalized Fiedler value ($\gamma$) of the Laplacian matrix, is critical for functional stability and energy efficiency. However, this property also renders networks vulnerable to targeted disruptions. Traditional percolation-based attack strategies, which focus on structural integrity, often fail to effectively suppress synchronization. This study introduces a Laplacian spectral perturbation approach to systematically identify and remove edges critical to synchronization. By deriving the sensitivity of $\gamma$ to topological changes and leveraging the gradient of the Fiedler vector, we quantify each edge's contribution to synchronization, revealing its connection to community structure. We propose the \emph{Fiedler Gradient Iterative Attack (FGIA)} algorithm for static networks, which constructs locally optimal edge removal sequences to maximize $\gamma$ degradation while preserving global connectivity. FGIA achieves computational efficiency, outperforming brute-force methods and conventional centrality-based attacks. Extensive simulations on synthetic and real-world networks demonstrate FGIA's superior performance in synchronization suppression, offering practical applications in neuroscience and critical infrastructure protection.

References in corpus (9)

• Synchronization in complex networks
• Synchronization in Complex Oscillator Networks and Smart Grids
• Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Remote synchronization reveals network symmetries and functional modules
• Chimera states: The Existence Criteria Revisited
• Network resilience
• Networkcontrology
• Hierarchical Synchronization and Distortion Scaling in Social Media Networks: A Fractal-Like Topology Theory