# The Influences of Self-Introspection and Credit Evaluation on Self-Organized Flocking
Some research on theoretical modeling considers that the interaction behavior between individuals and neighbors should be variable with time [32]. Therefore, the social networks of real biological groups should be weighted, which is reflected in the different levels of attention of individuals to their neighbors [33; 34], thus leading to different interaction strengths. Such an interaction mode has been proven to have an important impact on collective movement, and it is even closely related to effective information transmission between natural creatures [35; 36]. From the above considerations and inspiration, more detailed models are still needed to depict the interaction behaviors of real biological individuals. To this end, in this paper, we propose a framework consisting of two novel mathematical models to study the flocking behavior under different interaction mechanisms. Our two proposed models, the self-introspection model (SIM) and the credit evaluation model (CEM), focus on two different interaction mechanisms: _self-introspection_ and _credit evaluation_, respectively. The _self-introspection_ mechanism is motivated by the fact that some biological individuals can recognize the difference in orientations between themselves and neighbors within the scope of perception due to empirical learning [34; 37] and thus make an appropriate adjustment based on their own states. In our first model, the SIM, self-introspection is reflected in the orientation adjustment of the individual. If the local alignment perceived by individuals is relatively poor, then the adjustment of an individual orientation should be more significant. As the group gradually tends to be highly aligned, the smaller adjustment of an individual orientation is enough to achieve group stability. On the other hand, the second mechanism we focused on, the _credit evaluation_ mechanism, also comes from the observations of biological groups in nature. As the literature reveals, individuals are capable of evaluating the reliability or credibility of their neighbors through long-term group life and experience [38]. In some scenarios, some individuals' orientations maybe not be beneficial to achieving orientation consistency in groups. Therefore, the individual's evaluation of neighbors needs to be weighted according to their credibility, and the orientations of the neighbors with high credibility should be more valuable [39]. In our second model, the CEM, credit evaluation refers to the individual's evaluation of the credibility of his or her neighbor's orientation, where credibility characterizes the alignment between the neighbor and his or her neighbors. In both models, a common and key parameter is the alignment degree between individuals and their neighbors, which we call _local consistency_. Local consistency is one of the state attributes of individuals, and our proposed models, the SIM and CEM, are able to describe well the two interaction mechanisms of self-introspection and credit evaluation, respectively. We provide a detailed analysis of the two proposed models and determine the optimal parameters through numerical simulations. It is proven that both the group with the SIM and the group with the CEM achieve global consistency of the orientations more quickly than the group with the well-known Vicsek model (VM) and also have better performance against uncertain noise. Furthermore, mixed groups with these two different interaction mechanisms show better performance than that with a single behavior represented by the SIM in achieving the consistency of collective orientation. This is consistent with a common conclusion in nature, which is that behavioral differences between individuals play a fundamental role in promoting the movement and function of animal groups [40]. The rest of this paper is organized as follows. In Section 2, after introducing the well-known Vicsek model, we propose two novel mathematical models corresponding to two interaction mechanisms based on local consistency.