# Predator-Prey Model Based Asymmetry Resource Allocation in Satellite-Terrestrial Network
## 3 System Model  
In this section, we mainly discuss the asymmetry resource allocation problem in satellite-terrestrial network for 6G mobile communication. In the traditional satellite-terrestrial network, the network resources are mainly allocated among all the satellites based on the symmetry model, where the resources are allocated by the same optimal allocation model to achieve matching. This kind of symmetry model limits the increase of throughput. The researched satellite-terrestrial network is composed of multiple satellites and multiple mobile users, as shown in Figure 1. The mobile users can request and obtain the 6G mobile communication services from the satellites. The satellites can provide 6G mobile communication services to mobile users. With the development of the satellite-terrestrial network, increased satellites are utilized to provide access services to mobile users. As the communication and computation capacities of different satellites are different, they would have different services loads from the mobile users. Then, how to balance the services loads among the satellites is the key problem to be solved in this paper. In order to describe the load balancing problem of the proposed satellite network, we model the relationships between the satellites using the predator-prey model. Under the predator-prey model, we assume the satellites can be divided into two groups. The first group is the set of satellites with higher communication and computation capacities. This kind of satellite is always geosynchronous, with high orbits, and the transmission latency would also be high. Then, we assume that this kind of satellite cannot directly provide access services to mobile users due to high transmission latency. The second group is the set of satellites with limited communication and computation capacities. They are always the low-earth orbit satellites, and they can provide access services to mobile users with lower transmission latency. However, with limited communication and computation abilities, they should offload the service requirements of the mobile users to the satellites with higher communication and computation capacities because they cannot satisfy the increasing requirements of the mobile users, due to their limited capacities. Based on the above assumptions, the second satellites group should offload the services loads to the first satellites group. We will try to balance the services loads between these two kinds of satellite group. We use the predator-prey model to model the load balancing problem among different satellites. The satellite nodes with limited capacities are the prey-satellites denoted by \(s_{1}\), and the satellite nodes with higher capacities are considered as the predator-satellites  
Figure 1: System mode. denoted by \(s_{2}\). Assuming that, only the prey-satellites \(s_{1}\) can directly serve the mobile users. The predator-satellites \(s_{2}\) can only obtain the services loads offloaded from the prey-satellites \(s_{1}\). At time \(t\), assuming the services loads in the prey-satellites \(s_{1}\) is \(x_{1}(t)\). If the services load in the prey-satellites \(s_{1}\) are not offloaded to the predator-satellites \(s_{2}\), the dynamic variation of the services loads in the prey-satellites \(s_{1}\) can be described as follows [32],  
\[\frac{dx_{1}(t)}{dt}=[a_{1}(t)+\varepsilon_{1}u_{1}(t)]x_{1}(t) \tag{1}\]  
where \(a_{1}(t)\) is the variation rate of the services loads in the prey-satellites \(s_{1}\). \(u_{1}(t)\) is the action of the prey-satellites \(s_{1}\) to attract the mobile users to access to the satellite network, and \(\varepsilon_{1}\) is the related weighted parameter to denote the conversion percent of the action. At time \(t\), assuming the services loads in the predator-satellites \(s_{2}\) is \(x_{2}(t)\).