# Predator-Prey Model Based Asymmetry Resource Allocation in Satellite-Terrestrial Network
## 5 Numerical Simulations  
In this section, to verify the effectiveness of the load balancing model proposed in this paper, we use MATLAB to perform numerical simulations on the model. The hardware environment is Intel(R) Core(TM) i7-8550U CPU @ 1.80 GHz with 16.0 GB ram. The number of satellites in the simulation is two, which includes one prey-satellite and one predator satellite. The other simulation parameter settings are set in Table 1 as follows,  
The load states of a prey-satellite and predator-satellite without external stochastic factors are shown in Figure 2. Figure 2 shows a comparison between the prey-satellite and predator-satellite. The load state of the prey-satellite decreases quickly at the beginning of the load balancing process due to the load balancing action between the prey-satellite and the predator-satellite. The load state of the predator-satellite increases at the beginning of the load balancing process because the load of the prey-satellite is offloaded to the predator-satellite. With the increase of time, the load state of the prey-satellite tends to be stable. The load state of the predator-satellite decreases due to the decrease of the load in the prey-satellite. It can be seen that, for both the prey-satellite and predator-satellite, the models both changed rapidly based on the proposed predator-prey model from the initial moment and reached a stable state in the observation time duration.  
The load state with external stochastic factors for prey-satellites and predator satellites are given in Figure 3. Under the stochastic model, for both pre-satellite and predator-satellite, the models both reach a stable state in the observation time duration, which means that the proposed model can also achieve the same behaviors under the stochastic mode compared to the static mode in Figure 2. Under the external stochastic factors, the communication environments for mobile users would be different. Compared to the load state without external stochastic factors, the variation of load state with external stochastic factors are completely different. The load of the prey-satellite increases to a high value at the beginning of the time duration, then decreases to a convergence value due to the load  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline \(a_{1}(t)\) & 0.1 + 0.2 \(\times\) sin(pi \(\times\) k/15) \\ \(a_{2}(t)\) & 0.05 + 0.2 \(\times\) sin(pi \(\times\) k/15) \\ \(b_{1}\) & 0.1 \\ \(b_{2}\) & 0.18 \\ \(c_{1}\) & 0.4 \\ \(c_{2}\) & 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters for simulations.  
balancing process. The load of the predator-satellite also increases at the beginning of the time duration, due to the high value of the prey-satellite. It would also converge to a stable value. In Figures 2 and 3, it is assumed there are no actions of the satellites to attract mobile users to access to the satellite network.  
The load state of different satellites under stochastic control actions are given in Figure 4. Under the stochastic control actions, the prey-satellite and the predator-satellite decrease their load, and the load would converge to a stable value more quickly than the load without stochastic control actions. It can be concluded that both the prey-satellite and the predator-satellite can achieve sustainability under the stochastic control actions.  
Figure 3: Load state with external stochastic factors.  
Figure 2: Load state without external stochastic factors.