A Chemotaxis-Based Model for the Aggregation Behavior of Students

Understanding the aggregation behavior of high-achieving student groups is critical for optimizing educational resource allocation and upgrading institutional talent development systems. To address the prevailing gap in dynamic modeling for this specific phenomenon, this paper develops a two-equation chemotaxis-based framework to investigate the emergence and evolution of such aggregations. The first equation captures the dynamics of an attractiveness field shaped by peer learning attraction, knowledge gravity, and individual behavioral tendencies, while the second delineates the spatiotemporal evolution of the density of high-achieving students. Applying this framework, we first identify the parameter regimes that can generate hotspots of high-achieving students. Subsequently, well-posedness and stability analyses reveal a key insight: insufficient institutional management and incentive policies can lead to the gradual decline or even complete disappearance of these populations. This work thus contributes a theoretical model for understanding student group dynamics, while simultaneously providing educational institutions with a robust foundation for formulating inclusive and sustainable talent development strategies.