# The Influences of Self-Introspection and Credit Evaluation on Self-Organized Flocking
## 4 Conclusions  
In this paper, we explored two mechanisms that are ubiquitous in natural herds and human society. The mechanism of self-introspection reveals that an individual will take different efforts to catch up with others according to different gaps, while the mechanism of credit evaluation reflects the fact that an individual may assign different credits to different neighbors based on its evaluation. To evaluate these two mechanisms, we took the Vicsek model as the raw model and proposed two novel models, the SIM and CEM, by introducing the concept of local consistency. Using the SIM, the individuals decide the degree of effort to make turns according to their own local consistency. Using the CEM, the individuals determine the reference orientation by assigning different weights to their neighbors' orientations. In order to show the effectiveness of the two proposed models, numerical simulations were carried out for different models in both noise-free and noisy environments. We designed three metrics--the convergence time, the global consistency, and the cumulative global consistency--to evaluate the proposed models. It was found that there exists a quantitative relationship between the convergence time and the flocking parameters, and we further investigated the relationship between them and the model parameters. Based on the selected flocking parameters, the convergence time and cumulative global consistency were used as metrics to determine the optimal model parameters of the two proposed models. Then, under the optimal model parameters, the advantages of the two proposed models in terms of convergence efficiency were analyzed from the perspective of global consistency. However, when there was noise, the two models both showed poorer performance than that of the original Vicsek model. Furthermore, it was found through numerical simulations that the groups with mixed behaviors of the two proposed models had better performance compared with the groups with the single behavior of self-introspection. The findings obtained from this research may be valuable for the study of the mechanisms of individuals' behaviors in flocking in biology communities. Furthermore, this conclusion could also be applied to a distributed cluster of robots. Robotic swarms represent a distinct domain of entities. Both robotic swarms and biological swarms exhibit collective behaviors that self-organize through local perception among individuals, sharing many  
Figure 11: Final global consistency \(\phi\) evolves with noise \(\eta\) and individual action of self-introspection \(N_{I}/N\). \(N=300\) individuals move in a \(2D\) plane with \(L=5\), with a fixed speed of \(v=0.03\) and interaction radius of \(r=1\). Final global consistency \(\phi_{\eta}\) was obtained from the average of \(500\) independent runs. similarities in formation and behavior. While biological systems display higher complexity across multiple levels (from molecules to organ systems) and possess a certain evolutionary capacity, robots can mimic the behaviors of biological entities, responding to and making decisions based on the surrounding individuals or the environment. The individual behavior model proposed in this study can also be applied to robots, allowing the group to exhibit enhanced adaptability and robustness when adapting to their environment. Future work will concentrate on the more effective ways to combine these two mechanisms together to simulate flocking behaviors. Conceptualization, Q.Z. ; data curation, Y.L. ; formal analysis, Y.L. and S.L. ; funding acquisition, M.X. and G.X. ; investigation, S.L. and G.W. ; methodology, Q.Z. and Y.L. ; supervision, G.W. ; writing--original draft, Q.Z. and S.L. ; writing--review and editing, Q.Z., S.L. and C.W. All authors have read and agreed to the published version of the manuscript. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 51879022, 51979045, 51906029, 61973007, 12272008, and U22A2062), the Dalian Youth Star of Science and Technology (Grant No.