## 5 Analysis and Discussion  
Discussion 1: Experiments on Activated Boundary Cells in Different Scenarios  
In the experiments involving activated boundary cells in different scenarios, as the rat runs facing a wall, the number of activated boundary cells gradually increases, transitioning from the inhibition zone of boundary cells to the region of increased activity. When the rat moves away from the environmental boundary, the activation frequency of boundary cells gradually decreases (with a slower growth rate in the number of activated boundary cells). When the rat's motion corresponds to Figure 3d, exhibiting a trend of moving away from the environmental corner, the activation frequency of boundary cells gradually decreases. In an instantaneous motion similar to Figure 3d but with the difference that the rat is moving away from the environmental corner, and the restraining force from the environment decreases rapidly as the rat moves further from the boundary, the number of activated boundary cells temporarily enters a stage of slow growth. It can be observed that the activated boundary cells in different scenarios exhibit similar patterns as shown in Figure 4 (Activated Boundary Cells in Different Scenarios), aligning with the physiological observations. Furthermore, from the boundary cell response graphs at different time points in Figure 10, it can be observed that the proposed model can effectively model the boundary cells based on boundary information, regardless of the square or circular environment. As indicated by the boundary cell discharge response graphs captured at different time points in Figure 10, with the rat's comprehensive exploration of the environmental boundary, the number of activated boundary cells responding to the boundary continuously increases. Before 1600 s, the number of activated boundary cells exhibits a rapid increase, while after 1600 s, with the rat's comprehensive exploration of the environment, the growth rate of the number of activated boundary cells gradually slows down, approaching stability. At 1800 s, the activated boundary cells sufficiently represent the environmental boundary, and the number of activated boundary cells remains relatively stable, while the localization error stabilizes at around 0.37 m. This demonstrates the adaptability of the proposed method to larger circular environments, validating the effectiveness of the algorithm presented in this paper. Discussion 2: Validation Experiment on the Public Hafting Dataset  
The method proposed in this paper is validated using the square experiment dataset and the circular experiment dataset published by [PERSON] et al. in their paper \"Microstructure of a spatial map in the entorhinal cortex\" in Nature. The obtained position cell responses from the method proposed in this paper are compared with the position cell responses obtained from the competitive Hebbian learning network and the pose cell discharge response map obtained from RatSLAM. The RatSLAM algorithm only integrates self-motion information from the rat to activate pose cell responses at its current location, without fully considering the influence of simple geometric boundary cues on the discharge patterns of pose cells. Additionally, with the increase in exploration time response and  
Figure 13: Comparison of the performance of the three methods in terms of their spatial location representation maps. the growing environmental scene, cumulative errors gradually accumulate, resulting in RatSLAM's inability to generate a single pose cell that accurately responds to the current location. Compared to RatSLAM, the competitive Hebbian learning network can adjust the response values of position cells through the connection weights between them, enabling the system to maintain good localization performance in the early stages of exploration in unknown environments.