## 5 Conclusions  
Interference or space environmental factors may lead to time reference failure or time transfer link fault in the time-varying topology of LEO satellite networks [31]. In order to provide the long-distance time-sensitive services, it is necessary to recalculate the time synchronization transfer paths quickly; the means of a fast time synchronization of large-scale LEO satellite networks based on a bionic algorithm is illustrated in this paper. The ephemeris information from the navigation message is used to generate the connection table between satellites, which can obtain the current topology of the satellite network according to the connection table calculation results. In the PSO algorithm, six satellites are selected as the time sources, while the stratums of the time transfer trees are calculated. The minimum sum of the weighted layers is considered as the optimization objective to select the time sources. After the clock layers of the satellites in the network are determined, the time cascades of the satellites can be broadcasted to achieve fast and stable time re-synchronization. With the Iridium constellation topology, the PSO algorithm is compared with the traditional traversal algorithm. The optimization of PSO with the same result requires only 10 iterations, which is much smaller than the \(116\) iterations of the traversal algorithm, and significantly reduces the computational complexity. In this way, we can realize fast time synchronization in large-scale LEO satellite networks with time-varying topology, reduce clock synchronization levels, and decrease time synchronization jitters. In previous studies, various methods for the time synchronization of individual satellites are considered. These methods include satellite-to-ground bidirectional time synchronization, satellite-to-satellite time synchronization based on TWRTT technology, and time synchronization using global positioning system (GPS) or BeiDou navigation satellite system (BDS) navigation signals. For large-scale LEO satellite constellations, achieving time synchronization for all satellites is crucial. To ensure effective clock synchronization, the clock source must have high precision, necessitating careful selection of the clock source. Utilizing time synchronization methods based on GPS or BDS has the advantage of minimal error sources and high precision, making them the preferred choices for clock sources. In this study, we consider scenarios where environmental or human factors may impact the reception of navigation signals. In cases where navigation signals are unavailable or only a subset of satellites can receive them, it becomes necessary to select satellites within the current network as clock sources to accomplish time synchronization. In previous studies, when selecting a satellite as a clock source within a constellation, an iterative algorithm is utilized to compute all possible selection scenarios, compare their computational results, and select the optimal result. This study utilizes an iterative bionic algorithm, which significantly reduces the amount of computation. During simulation, we observed that the PSO algorithm occasionally converges to local optimal solutions without reaching the globaloptimum after 100 iterations. In the future, we plan to improve this algorithm or explore alternative algorithms to prevent it from becoming trapped in local optimal solutions. Conceptualization, Y.X. and J.Y. ; methodology, J.Y. ; software, Y.X. and H.J. ; validation, Y.X. and J.Y. ; formal analysis, T.D. ; investigation, T.D. ; resources, Z.L. ; data curation, Z.Z. ; writing--original draft preparation, Y.X. ; writing--review and editing, J.Y. and J.W. ; visualization, Z.Z. ; supervision, T.D. ; project administration, T.D. ; funding acquisition, T.D. All authors have read and agreed to the published version of the manuscript. This work was funded by National Key R&D Program of China (2022 YFB2902504). Not applicable.