# Information Propagation and Bionic Evolution Control of the _Sebar_ Model in a Swarm System
## 6 Experiences  
### Stability Analysis and Parameters Influence  
When discussing the stability of information dissemination and parameters' influences, \(R_{0}<1\) and \(R_{0}>1\) are considered, separately. For each situation, three sets of parameters are considered, as listed in Table 2. The maximum simulation step is 100, and the initial proportions of different states are \(S_{0}=0.95\), \(E_{0}=0\), \(B_{0}=0.05\), \(A_{0}=0\), and \(R_{0}=0\). From Table 2, it can be seen that the parameters in sets 1 to 3 correspond to the case of \(R_{0}<1\). According to previous analysis, when \(R_{0}<1\), the equilibrium point \(X_{1}\) is locally asymptotically stable. As depicted in Figure 4a, the proportion of the individuals in state \(S\) gradually approaches 1, while the proportion of those in states \(E\), \(B\), and \(A\) are nearly \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Group 1** & **Group 2** & **Group 3** & **Group 4** & **Group 5** & **Group 6** \\ \hline \(\langle k\rangle\) & 5 & 5 & 5 & 5 & 5 & 5 \\ \(p_{1}\) & 0.01 & 0.1 & 0.1 & 0.01 & 0.1 & 0.3 \\ \(p_{2}\) & 0.01 & 0.01 & 0.01 & 0.5 & 0.7 & 0.3 \\ \(p_{3}\) & 0.001 & 0.01 & 0.01 & 0.5 & 0.7 & 0.3 \\ \(p_{4}\) & 0.2 & 0.2 & 0.2 & 0.2 & 0.01 & 0.2 \\ \(p_{5}\) & 0.2 & 0.2 & 0.8 & 0.2 & 0.9 & 0.2 \\ \(p_{6}\) & 0.8 & 0.8 & 0.15 & 0.8 & 0.8 & 0.8 \\ \(p_{7}\) & 0.9 & 0.9 & 0.1 & 0.9 & 0.01 & 0.9 \\ \(p_{8}\) & 0.8 & 0.8 & 0.8 & 0.8 & 0.4 & 0.1 \\ \hline \(R_{0}\) & 0.1594 & 0.4688 & 0.7667 & 4.0938 & 9.7596 & 12.1875 \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters of the proposed model. Figure 3: State transition probability control function. 0. Therefore, the information in state \(B\) fails to spread throughout the network, and the simulation result is consistent with the stability analysis. By adjusting the model parameters (as listed in data sets 4 to 6), the case where \(R_{0}>1\) can be achieved, and the propagation characteristics of the information within the network can be given. As depicted in Figure 4b, the proportions tend to stabilize over time. This means that the information spread triggered by the individuals in state \(B\) is propagated continuously and stably. This also indicates that the equilibrium point \(X_{1}\) is non-locally asymptotically stable when \(R_{0}>1\). Taking the state transition path \(S\overset{B}{\rightarrow}E\to B\to R\to S\) as an example, the impacts of parameters \(p_{3}\), \(p_{5}\), \(p_{7}\), \(p_{8}\), and \(\langle k\rangle\) on the state \(B\) are discussed. This provides insights into the dynamic regulation of information propagation and evolution behaviors in swarm networks. The model parameters are shown in Table 3, and the simulation results are illustrated in Figure 5.  
Combined with previous analysis, when \(R_{0}<1\), the proportion of state \(S\) gradually approaches 1, while the proportions of states \(E\), \(B\), \(A\), and \(R\) converge to nearly 0. This indicates that the swarm system reaches stability. The propagation individuals disappear, and information loses its propagation capability and fails to disseminate. Similarly, when \(R_{0}>1\), the proportions of states \(S\), \(E\), \(B\), \(A\), and \(R\) tend to stabilize, and the information is continuously and stably propagated. As shown in Figure 5a, as \(p_{3}\) increases, the con  
Figure 4: Information propagation stability. (**a**) \(R_{0}<1\); (**b**) \(R_{0}>1\).