Given the structure of a large-scale complex network and the nodal dynamics are known, can we predict all the possible synchronization patterns to be emerged and, in addition, the conditions for generating these patterns? Whereas this question has been broadly interested and extensively studied, the existing methods require a priori knowledge of the network symmetries and, additionally, a perfect network symmetry. Recently, Huawei Fan, et al., proposed a general framework for exploring cluster synchronization behaviors in general large-size complex networks. The key of the new framework lies in the exploitation of the eigenvectors of the network coupling matrix, which has been largely overlooked in previous studies but in fact plays crucial roles in inferring the network dynamics. With the new framework, the authors are able to predict theoretically not only all the synchronization patterns to be emerged on the network, but also the critical couplings for generating the patterns and the sequence of the patterns in the transition to global synchronization. For more details, please refer to the article entitled “Eigenvector-based analysis of cluster synchronization in general complex network of coupled chaotic oscillators” by Huawei Fan, Ya Wang, and Xingang Wang, Front. Phys. 18(4), 45302 (2023).
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