# Information Propagation and Bionic Evolution Control of the _Sebar_ Model in a Swarm System
## 6 Experiences
### Stability Analysis and Parameters Influence
\begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**Fixed Parameters**} & **Adjustable Parameters** & \(\mathbf{R_{0}}\) \\ \hline Group 1 & \(p_{1}=0.01\) & \(p_{2}=0.01\) & \(p_{4}=0.2\) & & \\ Group 1 & \(p_{5}=0.2\) & \(p_{6}=0.6\) & \(p_{7}=0.6\) & \(p_{8}=0.08\) & \(p_{3}=[0.001,0.01,0.1,\) & \([0.1979,0.4792,3.2917,\) \\  & \(\langle k\rangle=5\) & & & \(0.3,0.5,0.7]\) & \(9.5417,15.7917,22.0417] \\  & \(p_{1}=0.01\) & \(p_{2}=0.01\) & \(p_{3}=0.3\) & & \\ Group 2 & \(p_{4}=0.2\) & \(p_{6}=0.6\) & \(p_{7}=0.6\) & \(p_{8}=0.08\) & \(p_{5}=[0.001,0.005,0.2,\) & \([0.4250,0.7825,9.5417,\) \\  & \(\langle k\rangle=5\) & & & \(0.3,0.5,0.9]\) & \(11.3833,13.4881,15.4015] \\  & \(p_{1}=0.01\) & \(p_{2}=0.01\) & \(p_{3}=0.3\) & & \\ Group 3 & \(p_{4}=0.2\) & \(p_{5}=0.3\) & \(p_{6}=0.6\) & \(p_{8}=0.08\) & \(p_{7}=[0.001,0.01,0.1,\) & \([11.3833,11.3833,\) \\  & \(\langle k\rangle=5\) & & & \(0.3,0.7,0.9]\) & \(11.3833,11.3833,11.3833\) \\  & \(p_{1}=0.01\) & \(p_{2}=0.01\) & \(p_{3}=0.3\) & & \\ Group 4 & \(p_{4}=0.2\) & \(p_{5}=0.3\) & \(p_{6}=0.6\) & \(p_{7}=0.6\) & \(p_{8}=[0.001,0.005,0.2,\) & \([90.1333,180.1333,4.633,\) \\  & \(\langle k\rangle=5\) & & & \(0.3,0.5,0.9]\) & \(3.1333,1.9333,1.1333] \\  & \(p_{1}=0.01\) & \(p_{2}=0.01\) & \(p_{3}=0.3\) & & \\ Group 5 & \(p_{4}=0.2\) & \(p_{5}=0.2\) & \(p_{6}=0.6\) & \(p_{7}=0.6\) & \(\langle k\rangle=[3,5,6,8,10]\) & \([6.8300,11.3833,13.6600,\) \\  & \(p_{8}=0.08\) & & & \(18.2133,22.7667]\) \\ \hline \end{tabular}
\end{table} 
Table 3: The influence of different parameters. vergence rate of state \(B\) noticeably accelerates, and the final proportion of state \(B\) also increases. From Figure 5b, it can be seen that the change trends are consistent with the parameter \(p_{3}\) when \(R_{0}<1\). In other words, the propagation states \(E\), \(B\), and \(A\) disappear, resulting in ineffective information dissemination. When \(R_{0}>1\) is larger, the proportions in the swarm system are gradually stabilized, which helps to create continuous and stable information propagation. Similarly, the convergence rate of the proportion of state \(B\) noticeably accelerates as \(p_{5}\) increases, and the proportion of state \(B\) also increases. Compared to the influence of parameter \(p_{3}\), the parameter \(p_{5}\) has a more significant impact on the final proportion of state \(B\). According to the basic reproduction number \(R_{0}\) and Table 3, it is evident that the parameter \(p_{7}\) does not affect the value of \(R_{0}\). Referring to Figure 5c, the larger \(p_{7}\) is, the higher the proportion of the state \(B\) before the swarm system reaches equilibrium. Under the influence of the forgetting mechanism, a larger \(p_{7}\) increases the possibility of the individuals in state \(R\) forgetting the received information, It also accelerates the state transfer from state \(R\) to state \(S\). Therefore, on the condition of \(R_{0}>1\), the proportion of the state \(B\) can be increased through adjusting this parameter properly. As shown in Figure 5d, when the \(p_{8}\) values are different, state \(B\) is significantly different and follows a similar trend to parameters \(p_{3}\) and \(p_{5}\). This means that the information fails to achieve effective dissemination when \(R_{0}<1\). On the contrary, when \(R_{0}>1\), information can be continuously and stably disseminated. From the perspective of the containment mechanism, a larger \(p_{8}\) results in a greater intensity of information suppression, and causes a slower convergence rate and smaller proportion of individuals to be in state \(B\). In addition, the impact of the \(p_{8}\) on the final proportion of individuals in state \(B\) is noticeably greater than that of \(p_{3}\), \(p_{5}\), or \(p_{7}\). In particular, when \(p_{8}=0.001\), the proportion of individuals in state \(B\) approaches 1. From the perspective of the network structure, \(\langle k\rangle\) affects the number of interactive neighbors.