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<p>This paper investigates exponential bipartite synchronization for cooperative-competitive neural networks with time-varying delays and subject to aperiodic Denial-of-Service (DoS) attacks. Unlike traditional studies that assume purely cooperative interactions or periodic attack patterns, this paper considers a more realistic and challenging scenario where both cooperative and competitive couplings coexist, modeled via signed graphs, and where DoS attacks occur aperiodically. By designing a control strategy and constructing a novel Lyapunov function, sufficient conditions for achieving bipartite synchronization under such adversarial environments are rigorously derived. A key theoretical contribution is the establishment of a maximum allowable duration for consecutive DoS attacks that preserves network stability. Furthermore, a piecewise analysis method integrating the contradiction principle with mathematical induction is proposed to verify the stability of the resulting system under aperiodic DoS attacks. Numerical simulations involving two numerical examples validate the effectiveness of the proposed control strategy and theoretical results, demonstrating robust synchronization performance even under competitive coupling and intermittent DoS attacks.</p>

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Bipartite Synchronization for Coupled Neural Networks Suffering from Denial-of-Service Attacks

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Shuo Liu,
  • Yunfei Ding,
  • Dong Ding

摘要

This paper investigates exponential bipartite synchronization for cooperative-competitive neural networks with time-varying delays and subject to aperiodic Denial-of-Service (DoS) attacks. Unlike traditional studies that assume purely cooperative interactions or periodic attack patterns, this paper considers a more realistic and challenging scenario where both cooperative and competitive couplings coexist, modeled via signed graphs, and where DoS attacks occur aperiodically. By designing a control strategy and constructing a novel Lyapunov function, sufficient conditions for achieving bipartite synchronization under such adversarial environments are rigorously derived. A key theoretical contribution is the establishment of a maximum allowable duration for consecutive DoS attacks that preserves network stability. Furthermore, a piecewise analysis method integrating the contradiction principle with mathematical induction is proposed to verify the stability of the resulting system under aperiodic DoS attacks. Numerical simulations involving two numerical examples validate the effectiveness of the proposed control strategy and theoretical results, demonstrating robust synchronization performance even under competitive coupling and intermittent DoS attacks.