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<p>In this study, a complex network rapidly switches between its restricted complement and itself while maintaining the network’s total weight. We show that by varying the switching duty cycle, the required coupling strength for network synchronization can be controlled and therefore optimized. The optimized coupling strength is smaller than either that of the original network and restricted complement. The analytical results are validated by simulating small and large random and scale-free (preferential attachment) networks of chaotic Hindmarsh–Rose neurons with 1–1 electrical coupling. Since the switching occurs at high frequency, the average topology can be considered, and the maximum conditional Lyapunov exponent of its variational equations and the synchronization error are calculated, serving as the synchronization criteria. The numerical results agree with the analytical basis and with each other. This study shows that rapid switching between the network and its restricted complement can create an effective average topology without requiring additional weight supplies, thereby controlling the system’s dynamic behavior at a layer between the two networks’ connection distributions. This is especially important for analyzing non-stationary networks and for designing structural control mechanisms.</p>

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Synchronization enhancement of complex networks by fast switching with their restricted complement

  • 期刊论文

  • 发表日期：

    2026年5月7日

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  • Atefeh Ahmadi,
  • Sajad Jafari,
  • Michael Small

摘要

In this study, a complex network rapidly switches between its restricted complement and itself while maintaining the network’s total weight. We show that by varying the switching duty cycle, the required coupling strength for network synchronization can be controlled and therefore optimized. The optimized coupling strength is smaller than either that of the original network and restricted complement. The analytical results are validated by simulating small and large random and scale-free (preferential attachment) networks of chaotic Hindmarsh–Rose neurons with 1–1 electrical coupling. Since the switching occurs at high frequency, the average topology can be considered, and the maximum conditional Lyapunov exponent of its variational equations and the synchronization error are calculated, serving as the synchronization criteria. The numerical results agree with the analytical basis and with each other. This study shows that rapid switching between the network and its restricted complement can create an effective average topology without requiring additional weight supplies, thereby controlling the system’s dynamic behavior at a layer between the two networks’ connection distributions. This is especially important for analyzing non-stationary networks and for designing structural control mechanisms.