## 1 Introduction
(2018) studied the application of optimal broadcasting algorithms in cascading failure propagation in interdependent networks, proposing distributed algorithms and centralized algorithms for node failure analysis. [PERSON] et al. (2018) proposed a small perturbation analysis method to identify abnormal nodes, enhancing network resilience against cascading failure attacks by controlling the abnormal nodes after an attack. The results also showed that increasing coupling strength can significantly improve network stability. [PERSON] et al. (2018) proposed a cascading failure model for interdependent networks, based on traffic redistribution under fluctuating loads, studying the impact of node tolerance and traffic distribution on network robustness. [PERSON] et al. (2018) studied the optimization problem of identifying critical nodes in interdependent networks, based on conditional risk values. The above-mentioned interdependent network cascading failure models have expanded the research methods for interdependent network cascading failures, but there is little research on cascading failures in air traffic control networks, both domestically and internationally. In this paper, based on the characteristics of cyber-physical systems and the actual operation of air traffic control networks, it is modeled as two interdependent complex networks. The cascading failure process of the air traffic control network is analyzed when attacking a certain node in the network, such as control positions, aircraft, reporting points, ground-air communication facilities, air traffic monitoring facilities, meteorological service facilities, etc., exploring its internal interdependencies, the process of initial failure nodes causing multiple dependent nodes to fail, and its internal failure propagation rules. Network attacks can have serious impacts on air traffic control networks, potentially leading to flight delays or cancellations, airport closures, compromising the safety of air traffic control networks, and causing safety and flight accidents. The cascading failure model can be used to address potential network attack threats by enhancing control capabilities, increasing the number of control positions, and implementing emergency response measures to counter network attacks and prevent cascading failures caused by network attacks. This article focuses on the resilience of air traffic control networks and constructs a cascading failure model, based on the complex interdependent network theory. Relevant concepts such as control cost are introduced to study the propagation process of cascading failures in interdependent networks, with a particular focus on the resilience of air traffic control networks under different interdependence parameter conditions between the control coordination network and the route facility network. A comparison is made with existing models, and the experimental results show that existing models simplify the fault evolution and network functional requirements, leading to an underestimation of cascading failures. To study the robustness of air traffic control networks and the impact of cascading failures, this article proposes optimization directions for air traffic control networks, providing guidance for them to resist cascading failure attacks and enhance their resilience. The rest of the article is organized as follows: In Section 2, the cascading failure model for air traffic control networks is constructed. Section 3 discusses the propagation process of the cascading failure model in detail, while Section 4 presents the experimental results and discussion. Finally, Section 5 summarizes the conclusions.