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Synchronization of stochastic delayed dynamical networks with directed event-based couplings

Author

Listed:
  • Jia, Qiang
  • Liu, Zirong
  • Jiao, Ticao
  • Cai, Shuiming

Abstract

This study investigates the synchronization issue for a network of delay nonlinear systems over a directed graph, where the systems suffer from certain stochastic noises, and their couplings follow a directed graph. By utilizing the pinning control technique, some effective protocol is developed with certain event-triggering mechanism, and the problem is recast into the stability of a delay differential equation with both stochastic noise and deterministic perturbation. In order to solve the problem, a novel Lyapunov–Krasovskii functional is designed, and a criterion is derived to guarantee synchronization in mean square sense. Zeno behaviors are also excluded with strict mathematical proof. A novel finding from the theoretical result is that given a fixed coupling strength, stochastic noise with large intensity may devastate synchronization even for an extremely large pinning effort. Besides, the well-known Braess’s paradox in traffic networks is also numerically observed herein, i.e., adding some new edges may possibly impair synchronization. Finally, numerical examples are also given to validate the theoretical results and illustrate the performance of the proposed control scheme.

Suggested Citation

  • Jia, Qiang & Liu, Zirong & Jiao, Ticao & Cai, Shuiming, 2025. "Synchronization of stochastic delayed dynamical networks with directed event-based couplings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    • Handle: RePEc:eee:phsmap:v:658:y:2025:i:c:s0378437124007829
    DOI: 10.1016/j.physa.2024.130272
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