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<p>This paper investigates global exponential synchronization and ultimate boundedness for complex-valued neural networks (CVNNs) with distributed delays over directed topologies. The main challenge comes from asymmetric coupling, distributed memory, and intrinsic amplitude–phase coupling, which make communication efficient synchronization nontrivial. Instead of converting CVNNs into augmented real systems, the analysis is performed directly in the complex domain by using Hermitian products, complex-valued Jacobians, and matrix measures. A reactivity-aware event-triggered control (RAETC) scheme is proposed, where transverse reactivity and an auxiliary dynamic variable regulate the triggering threshold to capture transient perturbation amplification. A non-fragile zero-order hold state feedback controller is designed to tolerate bounded gain perturbations. By combining complex domain estimates, Jensen inequalities, and a Halanay-type comparison argument retaining the exponentially decaying triggering term, sufficient conditions are derived for global exponential synchronization with an explicit convergence rate. Under bounded disturbances, an ultimate synchronization error bound is obtained, and finite-time Zeno behavior is excluded. Simulations on synchronization, disturbance rejection, and image encryption verify the results. Ablation and comparison tests show that RAETC reduces triggering events from 506 and 825 to 379 compared with MVET-SC and HMAS-based schemes, while preserving balanced synchronization and communication performance.</p>

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Reactivity-aware event-triggered synchronization and ultimate boundedness of delayed complex-valued neural networks over directed topologies

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Bole Li,
  • Dongfu Hou,
  • Yang Song,
  • Fanrong Sun

摘要

This paper investigates global exponential synchronization and ultimate boundedness for complex-valued neural networks (CVNNs) with distributed delays over directed topologies. The main challenge comes from asymmetric coupling, distributed memory, and intrinsic amplitude–phase coupling, which make communication efficient synchronization nontrivial. Instead of converting CVNNs into augmented real systems, the analysis is performed directly in the complex domain by using Hermitian products, complex-valued Jacobians, and matrix measures. A reactivity-aware event-triggered control (RAETC) scheme is proposed, where transverse reactivity and an auxiliary dynamic variable regulate the triggering threshold to capture transient perturbation amplification. A non-fragile zero-order hold state feedback controller is designed to tolerate bounded gain perturbations. By combining complex domain estimates, Jensen inequalities, and a Halanay-type comparison argument retaining the exponentially decaying triggering term, sufficient conditions are derived for global exponential synchronization with an explicit convergence rate. Under bounded disturbances, an ultimate synchronization error bound is obtained, and finite-time Zeno behavior is excluded. Simulations on synchronization, disturbance rejection, and image encryption verify the results. Ablation and comparison tests show that RAETC reduces triggering events from 506 and 825 to 379 compared with MVET-SC and HMAS-based schemes, while preserving balanced synchronization and communication performance.