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<p>We study the emergent asymptotic dynamics of coupled Kuramoto–Winfree model on multiplex networks consisting of two-layer planar graphs. The proposed synchronization model also admits a gradient flow formulation via vertical sinusoidal coupling between Kuramoto and Winfree oscillators. Due to this inter-layer coupling, the Kuramoto–Winfree model loses a continuous translation invariance property so that the total sum of Kuramoto phases does not satisfy a balance law. However, we can still keep the gradient flow formulation even for the inter-layer couplings. We provide several frameworks in terms of system parameters and initial configurations which lead to emergent asymptotic patterns such as complete synchronization, existence of equilibrium and existence of bounded sub-ensemble. We also present several numerical examples and compare them with analytical results.</p>

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On Emerging Asymptotic Patterns in a Kuramoto–Winfree Ensemble on Multiplex Networks

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Jiu-Gang Dong,
  • Seung-Yeal Ha,
  • Myeonghyeon Kim,
  • Wen Sun,
  • Yu-Qing Wang

摘要

We study the emergent asymptotic dynamics of coupled Kuramoto–Winfree model on multiplex networks consisting of two-layer planar graphs. The proposed synchronization model also admits a gradient flow formulation via vertical sinusoidal coupling between Kuramoto and Winfree oscillators. Due to this inter-layer coupling, the Kuramoto–Winfree model loses a continuous translation invariance property so that the total sum of Kuramoto phases does not satisfy a balance law. However, we can still keep the gradient flow formulation even for the inter-layer couplings. We provide several frameworks in terms of system parameters and initial configurations which lead to emergent asymptotic patterns such as complete synchronization, existence of equilibrium and existence of bounded sub-ensemble. We also present several numerical examples and compare them with analytical results.