## 1 Introduction  
With the development of complex dynamical network theory and its application in recent years, complex dynamical networks (CDNs) have become a hot research topic in many fields [1]. CDNs are composed of many nodes and edges, which are used to represent different individuals and connections between individuals. In particular, it is of great importance to investigate the connection of edges and the communication of nodes. In recent years, CDNs have been widely used to simulate many large-scale practical complex projects [2; 3; 4; 5; 6]. Many topics on CDNs have been discussed, including synchronization, propagation dynamics and fault diagnosis, control and network model [7; 8; 9; 10; 11; 12; 13], etc. On the other hand, complex cyber-physical networks (CCPNs) as a special type of CDNs have received extensive attention. CCFNs are multi-dimensional complex systems consisting of computing network and physical environment, which realize the integrated design of computing communication and physical systems. Therefore, it has a wide application prospect, such as medical science, transportation networks, electric power grid and manufacturing [14; 15; 16; 17; 18; 19; 20]. Many interesting issues on CCPNs have been intensively investigated in the literature. Specially, the synchronization problem of CCPNs has been discussed in [21; 22; 23; 24; 25]. Due to high dependence on networks, CCFNs are faced with many cyber attack threats. Typical cyber attacks main contain false data injection (FDI) attacks and denial-of-service (DoS) attacks [15; 21; 26; 27]. Attackers use cyber attacks to interfere with the information space of the system or destroy data, which can affect the physical space of the system and even destroy the whole system. In particular, DoS attacks can block the transmission links of networks such that the transmission information received by actuators and sensors can be corrupted, thereby affecting the system performance. Many research studies have been reported on the security of cyber-physical systems (CPSs) under DoS attacks. For example, the event-triggered secure control for multi-agent systems with DoS attacks was investigated in [28; 29; 30; 31; 32; 33], in which a multi-robot model was proposed in [30], keeping all six robots in a line and achieving the consensus of their position and velocity under the designed event-triggered control (ETC) strategy. The distributed controller was designed for CPSs with communication delays against attacks in [34; 35; 36]. Unfortunately, the above existing results only discussed the convergence of the systems based on the controller and did not investigate the strong coupling between individuals within the systems. That is, the security synchronization control has not been fully investigated for CCPNs, which have highly coupled nodes and intricate communication links, making it difficult to solve. This motivates the present work. In this paper, a distributed event-triggered control strategy is proposed for CCPNs to update the state transmission under DoS attacks, which relieves the communication occupancy rate of limited bandwidths and achieves synchronization of all the nodes. The following are the contributions of this paper:  
(1) A distributed controller is designed to achieve all nodes of CCPNs are synchronized under DoS attacks, which uses two combinational measurements of isolated node and follower nodes. (2) An ETC strategy is proposed to save communication resources under DoS attacks. Different from [25; 28; 30; 36], triggering behavior and Zeno behavior are both excluded in this paper, which avoids continuous triggering in each verification cycle and guarantees that certain data are still transmitted after a successful transmission attempt. (3) A resilient event-triggering mechanism is constructed to tolerate packet loss and topologies change under DoS attacks. Attack duration and frequency can be calculated to describe attack behavior based on piecewise Lyapunov functions.