## 1 Introduction  
The mobile wireless network is a self-organized, centerless, dynamic topology, and mobile distributed network, which has the advantages of strong mobility, fast networking speed, the ability to adapt to harsh environments, and strong robustness [1]. It is widely used in fields such as disaster reconstruction, UAV scientific research, military warfare, and other fields. Nodes' mobility is one of the most significant characteristics of UAV ad hoc networks [2]. Various performance indicators of the network, such as throughput, transmission delay, and routing effectiveness, are closely linked to the mobility of nodes. In UAV wireless networks, node mobility can bring greater sensing ranges, more opportunities for information interactions, and more flexible network services and applications [3]. However, node mobility also brings many problems. The movement of nodes can lead to frequent changes in network topology, which directly affects network performance, such as energy consumption, communication capacity, routing performance, etc., specifically reflected in packet loss, throughput reduction, and even network segmentation. To simulate the complex and variable motion states of nodes, mobility models are therefore proposed to describe the movement patterns, such as node position coordinates, movement speed, acceleration changes, and other information, which is an abstraction of the motion of nodes. Currently, a variety of node mobility models have been proposed, and studies have shown that different mobility models have different effects on the performance of the network protocols and algorithms [4]. As the basis for performance evaluation and network designing of related systems, protocols, and algorithms in mobile ad hoc networks, the research on network node mobility models is of great importance for improving UAV network performance. Mobility models are important baselines in network simulation to describe the movement of nodes, including changes in their position, velocity, and acceleration. The design and research of mobility models serve as the foundation for the development and application of various protocols and technologies in UAV ad hoc networks, which will help researchers gain a better understanding of network performance and potential issues, thereby promoting the specific implementation and performance improvement in networks. In the research process of mobility models, it is common to introduce or propose a mobility model, then analyze the various characteristics of the model combined with specific connectivity evaluation methods to conduct a theoretical analysis or verify through experiments, and finally, obtain the network connectivity performance under the mobility model [5]. Ref. [6] brought forth a metric, the lifetime of link topology, to evaluate the dynamic characteristics of an ad hoc network. From the analysis of the simulation data of three classical mobility models, it can be seen that the link topology snapshots method is not only a new idea to obtain the link topology lifetime of an ad hoc network but also the ratio of link connection, the variety ratio of link topology, and the link topology lifetime curve could be derived. The movement of nodes in a network mainly depends on the network's mobility model. In the early days, the random waypoint (RWP) model [7], the random walk (RW) model [4], and other mobility models were often used to simulate the movement of nodes to analyze the relevant characteristics of the network. [PERSON]. [8] analyzed network connectivity performance based on the RWP model and provided an approximation of the probability that the network becomes k-connectivity. In addition, it was also found that when the network is sparse, the mobility of nodes has a positive impact on the connectivity probability of the network, while for dense networks, the opposite is true. Meanwhile, the average connection time of a network also greatly affects network connectivity probability. Based on percolation theory, Ref.