标题： 等价性和爆炸性同步在多路和高阶网络中的表现 显示英文标题

标题： Equitability and explosive synchronisation in multiplex and higher-order networks

摘要： 集群同步是在耦合动力单元网络中观察到的关键现象。 其存在与对称性有关，并且更一般地，与相同动力单元之间相互作用的基础网络模式的等价性有关。 在本文中，我们彻底澄清了等价性与集群同步之间的关系，在一个允许多层和高阶相互作用的非常一般的动力系统中。 具体来说，我们证明等价性是独立集群同步解存在的必要且充分条件。 作为重要的结果，我们的研究结果解释了在多层和高阶网络中爆炸性同步而非集群同步的普遍性：等价性在相同节点集上施加了必须同时满足的额外约束。 我们的研究结果对于设计具有任意集群同步模式和耦合函数的耦合动力单元复杂动力系统具有重要意义。 显示英文摘要

摘要： Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying network pattern of interactions between identical dynamical units. In this article, we clarify once and for all the relation between equitability and cluster synchronisation on a very general dynamical system which allows multi-layer and higher-order interactions. Namely, we show that equitability is a necessary, and sufficient, condition for the existence of independent cluster synchronised solutions. As an important consequence, our results explain the ubiquity of explosive synchronisation, as opposed to cluster synchronisation, in multi-layer and higher-order networks: equitability imposes additional constraints that must be simultaneously satisfied on the same set of nodes. Our results have important implications for the design of complex dynamical systems of coupled dynamical units with arbitrary cluster synchronisation patterns and coupling functions.