在网络中进行拓保护的同步
1Universidade Federal da Bahia, Instituto de Física, Salvador, BA 40170-115, Brazil.
Physical review. E
|November 18, 2025
概括
图形中的拓等价节点可以在形成连接子图时轻松同步,作为独立的节拍器. 这种同步独立于其他节点和图形变化.
科学领域:
- 图形理论 图形理论
- 网络科学 网络科学
- 非线性动力学是一种非线性动力学.
背景情况:
- 在图形中的拓等价性是由相吻合的邻居集定义的.
- 合振荡器的同步是网络科学中的一个关键问题.
- 不同质的振荡器为同步现象带来了复杂性.
研究的目的:
- 研究在拓上等价节点上的非线性合异质振荡器的同步行为.
- 确定在这些组内可以实现同步的条件.
- 分析同步的稳定性,以应对网络其余部分的变化.
主要方法:
- 数学证明建立了同步的条件.
- 对图形属性的分析,特别关注节点社区.
- 数字模拟用于验证理论发现.
主要成果:
- 在拓上相当的节点上的非线性合异质振荡器,如果它们形成一个完全连接的子图,就很容易同步.
- 集团内部的同步是独立于集团外的振荡器.
- 当内部度小于或等于输出度 (k_IN <= k_OUT) 时,通常可以实现同步.
结论:
- 拓上相当的节点组可以在更大的网络中作为独立的同步单元或节奏器.
- 这些组的同步状态对更广泛的网络结构的变化具有强大耐受性.
- 这些发现为复杂网络中可预测的同步提供了理论框架和基于模拟的证据.
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