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<p>This paper explores exponential bipartite synchronization in multilayer signed networks, where intra-layer connections may exhibit positive or negative weights. In contrast to existing studies, this work incorporates both proportional time delays and the complexity of multilayer network topologies. Under the assumption that each layer’s signed graph is structurally balanced, a fuzzy adaptive controller is designed to drive the network toward synchronization. Several key lemmas and sufficient conditions are established to guarantee exponential bipartite synchronization. Numerical simulations are conducted to verify the theoretical findings, and the proposed approach is further demonstrated through its application to image protection.</p>

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Exponential bipartite synchronization of multilayer signed networks with proportional delays for image protection

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Junren Wang,
  • Junjian Huang,
  • Yao Tan,
  • Tieshan Li,
  • Shiping Wen,
  • Tingwen Huang

摘要

This paper explores exponential bipartite synchronization in multilayer signed networks, where intra-layer connections may exhibit positive or negative weights. In contrast to existing studies, this work incorporates both proportional time delays and the complexity of multilayer network topologies. Under the assumption that each layer’s signed graph is structurally balanced, a fuzzy adaptive controller is designed to drive the network toward synchronization. Several key lemmas and sufficient conditions are established to guarantee exponential bipartite synchronization. Numerical simulations are conducted to verify the theoretical findings, and the proposed approach is further demonstrated through its application to image protection.