Department of Electrical and Electronics Engineering, Dokuz Eylül University, İzmir 35390, Turkey.
Chaos. 2020 Jun;30(6):063127. doi: 10.1063/1.5139695.
It is known that chaotic dynamical systems in the coupled networks can synchronize, and they can even form clusters. Our study addresses the issue of determining the membership information of continuous-time dynamical networks forming clusters. We observe the output vectors of individual systems in the networks and reconstruct the state space according to Takens' embedding theorem. Afterward, we estimate the information-theoretic measures in the reconstructed state space. We propose the average integrated causation entropy as a model-free distinctive measure to distinguish the clusters in the network using the k-means clustering algorithm. We have demonstrated the proposed procedure on three networks that contain Chua systems. The results indicate that we can determine the members of clusters and the membership information from the data, conclusively.
已知耦合网络中的混沌动力系统可以实现同步，甚至可以形成簇。我们的研究解决了形成簇的连续时间动力网络的成员信息确定问题。我们观察网络中各个系统的输出向量，并根据 Takens 嵌入定理重建状态空间。之后，我们估计重建状态空间中的信息论度量。我们提出平均积分因果熵作为一种无模型的独特度量，使用 k-means 聚类算法来区分网络中的簇。我们已经在包含 Chua 系统的三个网络上验证了该方法。结果表明，我们可以从数据中确定簇成员和成员信息。
