耦合相位振荡器同步的高阶网络拓扑优化
Optimizing higher-order network topology for synchronization of coupled phase oscillators
摘要：
自然界中的网络具有代理之间的复杂交互。由交互引起的一个重要现象是耦合代理的同步，并且交互网络拓扑可以被调整以优化同步。以往的研究表明，优化的传统网络与成对的相互作用有利于均匀的度分布的节点时，相互作用是无向的，总是结构不对称的，当相互作用是有向的。然而，最优控制的同步与普遍的高阶相互作用的网络较少探索。在这里，通过考虑超图中的高阶相互作用和具有2-超链接相互作用的Kuramoto模型，我们发现具有优化同步性的网络拓扑可能具有不同的性质。对于无向交互，通过模拟退火优化的具有2-超链接交互的网络倾向于在节点的广义度上变得均匀，与1-超链接（成对）交互一致。我们进一步定义了有向超链接，并严格证明了对于有向交互，具有2-超链接交互的最佳同步网络可以保持结构对称性，这与1-超链接交互的结论相反。结果表明，控制网络拓扑结构的高阶相互作用导致同步现象超越成对的相互作用。
英文摘要：
Networks in nature have complex interactions among agents. One significant phenomenon induced by interactions is synchronization of coupled agents, and the interactive network topology can be tuned to optimize synchronization. The previous studies showed that the optimized conventional network with pairwise interactions favors a homogeneous degree distribution of nodes when the interaction is undirected, and is always structurally asymmetric when the interaction is directed. However, the optimal control on synchronization for networks with prevailing higher-order interactions is less explored. Here, by considering the higher-order interactions in hypergraph and the Kuramoto model with 2-hyperlink interactions, we find that the network topology with optimized synchronizability may have distinct properties. For the undirected interaction, optimized networks with 2-hyperlink interactions by simulated annealing tend to become homogeneous in the nodes' generalized degree, consistent with 1-hyperlink (pairwise) interactions. We further define the directed hyperlink, and rigorously demonstrate that for the directed interaction, the structural symmetry can be preserved in the optimally synchronizable network with 2-hyperlink interactions, in contrast to the conclusion for 1-hyperlink interactions. The results suggest that controlling the network topology of higher-order interactions leads to synchronization phenomena beyond pairwise interactions.
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