Hyperedge-Based Adaptive Pinning Control in Hypernetworks Under Dynamic Link Attacks

Abstract

Ensuring synchronization in networked systems presents a growing challenge, particularly for complex systems characterized by higher order interactions extending beyond pairwise connections. In this article, we investigate a class of hypernetwork systems in hypergraphs and introduce a novel dynamic link attacks that allow dynamic attack patterns on hyperedges. To address the vulnerability of the higher order systems under these conditions, we propose a hyperedge-based adaptive pinning control strategy to guarantee synchronization in hypernetworks with time-varying couplings. Based on the original hypergraph topology, an augmented hypergraph is constructed by establishing pinning hyperedges between tracking and pinning nodes. Concurrently, a time-varying adaptive coupling mechanism is further designed, which dynamically adjusts the strengths of both standard and pinning hyperedges based on local synchronization errors. Utilizing the Lyapunov function method, sufficient conditions guaranteeing exponential synchronization are derived. Finally, the effectiveness of the proposed strategy is demonstrated through numerical simulations on a nonlinear hypernetwork composed of chaotic Chua’s circuit.