# The Influences of Self-Introspection and Credit Evaluation on Self-Organized Flocking
## 3 Simulations and Discussions
### Noise-Free Calculation and Analysis
#### 3.1.3 Model Comparison  
Our two proposed models not only depict the interaction mechanisms of individuals in detail but also show advantages in the convergence efficiency. In the absence of noise, the convergence time \(T\), global consistency \(\phi\), and cumulative global consistency \(S\) are discussed to compare the proposed models with the Vicsek model. Figure 8: Variation in \(\alpha_{\text{opt}}\), \(\beta_{\text{opt}}\) measured by cumulative global consistency \(S\) against \(N\), \(v\), and \(r\). Selected flocking parameters: \(N=300\), \(v=0.03\), and \(r=1\). In the subgraph, two parameters are fixed, and another parameter changes within a certain range. Each point was obtained from the average of 500 independent noise-free runs. Figure 7: Variation in \(\alpha_{\text{opt}}\), \(\beta_{\text{opt}}\) measured by convergence time \(T\) against \(N\), \(v\), and \(r\). Selected flocking parameters: \(N=300\), \(v=0.03\), and \(r=1\). In the subgraph, two parameters are fixed, and another parameter changes within a certain range. Each point was obtained from the average of 500 independent noise-free runs. As shown in Figure 5, there is the remarkable fact that within a certain parameter range, both of the proposed models were superior to the original Vicsek model in terms of the convergence time when the number of individuals and their interaction radius were the same; that is, by using the SIM or CEM, the convergence was accelerated. This conclusion can also be drawn from the previous discussion of the relationship between the optimal parameters of the models and the flocking parameters. For instance, Figures 7a and 8a show that the two proposed models had more advantages in terms of convergence time and the cumulative global consistency than the original Vicsek model (\(\alpha=\beta=0\)), except for \(v\geq 1.2\). Figures 7b and 8b can also lead to similar conclusions. In particular, as shown in Figures 7c and 8c, the advantages of the proposed model can be reflected in the case of a fixed speed and interaction radius, regardless of the density of the group. In order to compare the convergence efficiency of different models more intuitively, we carried out specific simulations of different models under a set of flocking parameters, where the SIM and CEM were under their optimal model parameters, and the global consistency \(\phi\) was used as the metric. The flocking parameters \(v=0.03\), \(N=300\), and \(r=1\) were selected, and then the optimal model parameters of the SIM and CEM were \(\alpha=1.7\) and \(\beta=1.4\), which could be obtained from Figure 8. The result is shown in Figure 9. This result shows that under the above parameter conditions, the two proposed interaction mechanisms were superior to the [PERSON] model in terms of global consistency \(\phi\), and the self-introspection was superior to that of the credit evaluation. Here, we want to emphasize the changes in the convergence efficiency of the three models in Figure 9. In the first 3\(\sim\)4 s, the convergence efficiency of the CEM was the highest, and that of the SIM was the lowest. However, the SIM caught up with the other two models after 4 s, which is one of the reasons why the model had different performance under the two metrics \(T\) and \(S\). The threshold \(\phi_{\text{thre}}\) obviously not only determined the convergence time but also affected the value of the cumulative global consistency. Therefore, the convergence time \(T\) reflects the final performance of a model, while the cumulative global consistency \(S\) focuses on the comprehensive performance of the whole process. From Figure 9, it can be seen that the individuals with self-introspection (SIM) could not find a superior way of adjusting the orientation for themselves in the early stage, but with the narrowing of the difference between the movement orientation and the average orientation of their neighbors, they gradually adapted to the orientation consistency of the group and effectively corrected the orientation.