# Robustness of Double-Layer Group-Dependent Combat Network with Cascading Failure
## 5 Conclusions  
The phenomenon of cascading failure in the DGCN of CSOS will lead to a complete collapse of the system in the face of a relatively small proportion of damage, resulting in the loss of combat effectiveness. Therefore, finding out the reasons that affect the robustness of the combat network and improving the system's capability to further stop the collapse are of great significance. In this paper, we contribute some results as follows:  
(1) We established a more realistic combat network model of the DGCN of CSOS. (2) We designed the cascading failure model of the DGCN by combining the asymmetric dependent failure, conditional group-dependent failure, and overload failure together. We also designed the load reallocation strategy and a more practical robustness index. (3) We investigated the robustness of the combat network with six different attack modes and different model parameters. The simulation results show that the robustness of the combat network can be effectively improved by improving the tolerance limit of one-way dependency of the functional net, the node capacity of the functional net, and the tolerance of the overload state. When the attack intensity remains steady, the combat network's ability to deal with deliberate attacks is weaker than that with random attacks,  
Figure 13: Robustness with different \(\delta\). Panels (**a–c**) represent the robustness under different \(\delta_{\text{G}}\) when the subnet is ER-net, Goh-net, and NW-net, respectively; (**d–f**) represent the robustness under different \(\delta_{\text{W}}\) when the subnet is ER-net, Goh-net, and NW-net, respectively. and for different attack methods, different model networks perform inconsistently. It is necessary to design a reasonable network structure to enhance the antidestruction ability of the combat network. The model established in this paper is more real, and the laws concluded from the simulation experiments have certain reference significance for optimizing the structure of the combat network and improving the robustness of CSOS. The merits and demerits of our method compared with other methods are listed in Table 11. However, there are still some limitations to our study. For one thing, combat networks are modeled statically and only a single type is considered in the overall combat network; for another, there is a lack of data on real combat networks for reasons of secrecy. Therefore, we are going to conduct more research work in the future:  
(1) Investigate the impact of collocation of different model networks on robustness;  
(2) Obtain the real combat network data in some special situations and verify the effectiveness of the model on real data. Conceptualization, J.Y. ; methodology, J.Y. ; software, J.Y. ; validation, J.Y. ; formal analysis, J.Y. ; investigation, J.Y. ; resources, J.Y. ; data curation, J.Y. ; writing--original draft preparation, J.Y. ; writing--review and editing, J.Y. and Y.C. ; visualization, J.Y. ; supervision, B.X. ; project administration, J.Y. ; funding acquisition, J.Y. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China under Grant No. 61502522 and National University of Defense and Technology Research Program under Grant No. JS20-10. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the restricted access to public repositories. The authors would like to express appreciation to the anonymous reviewers and journal editors for their contributions to the smooth publication of this article. The authors also would like to thank the funding support provided by National Natural Science Foundation of China and National University of Defense and Technology. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: