Cluster synchronization in mutually-coupled semiconductor laser networks with different topologies

The cluster synchronization properties of 12 different networks that consist of five semiconductor lasers (SLs) are systematically investigated through theoretical analysis and numerical simulation. The emergence of clusters in different networks is analytically predicted, and then numerically proved in SL networks. The synchronization properties between each pair of SL nodes in a network are quantified by the zero-lag cross-correlation coefficient of laser intensities. The impacts of injection strength and bias current on the synchronization quality are investigated, the robustness of clusters against noise is also considered. All the expected clusters are successfully obtained in the simulation and are robust to noise. However, for some networks, different clusters may also emerge with the variation of parameters. In addition, for most networks considered in this paper, the small difference in topologies can bring about tremendous change in synchronized clusters or the synchronization properties of clusters, but for other networks no obvious change can be observed. Moreover, the synchronization properties between nodes from different clusters are also considered. The numerical results not only validate the availability of the adopted analytical method, but also shed some light on possible applications of synchronization control or tolerance of connection failure within networks of SLs.