同步模式表征网络的一种状态，其中节点依据其同步动力学组织为若干簇。这些同步簇可进一步呈现活性或非活性状态。同步节点的活性簇与非活性簇同时保持不变，构成一种动力学约束：活性簇产生的涨落必须相互抵消，才能使某一特定簇维持非活性状态。我们通过利用网络结构中的置换对称性，并选取相空间中内部动力学与耦合函数均为奇函数的动力学形式，证明该结构与动力学的组合可产生由共存的活性簇与非活性簇构成的稳定不变模式。网络中的对称性导致活性簇彼此处于反同步状态，从而使与这些反同步簇相连的簇所受涨落相互抵消。我们利用全网络对称性确定同步簇，而利用商网络对称性识别簇的共存活性-非活性状态。结果表明，随着节点间耦合强度变化，各活性簇在不同耦合值处相继失去活性，网络由此在不同活动模式之间发生转变。文中以范德波尔（Van der Pol）振子与斯图尔特-兰道（Stuart-Landau）振子网络为例进行了数值模拟。最后，我们将主稳定性框架（master stability framework）推广至此类模式，并给出了其存在的稳定性条件。

Synchrony patterns characterize network states in which nodes organize into clusters based on their synchronized dynamics. The synchronized clusters may further exhibit either active or inactive states. The simultaneous invariance of active and inactive clusters of synchronized nodes poses a dynamical constraint because fluctuations from active clusters must cancel out for a desired cluster to be inactive. By exploiting permutation symmetries in the network structure and choosing dynamics on top such that internal dynamics and coupling functions are odd functions in the phase space, we demonstrate that this combination of structure and dynamics exhibits stable invariant patterns composed of coexisting active and inactive clusters. The symmetries in a network generate active clusters that are in antisynchrony with each other, resulting in the cancellation of fluctuations for clusters connected with these antisynchronous clusters. We use full network symmetries to obtain synchronized clusters, while quotient network symmetries are used to find coexisting active-inactive states of clusters. We show that as the coupling between nodes changes, active clusters lose their activity at different coupling values, and the network transitions from one activity pattern to another. Numerical simulations are presented for networks of Van der Pol and Stuart-Landau oscillators. Finally, we extend the master stability framework to these patterns and provide stability conditions for their existence.