# The Role of Sensory Cues in Collective Dynamics: A Study of Three-Dimensional Vicsek Models
## 4 Discussion  
In this study, we introduce a three-dimensional collective motion model that integrates auditory and visual sensing modalities, inspired by organisms like bats that use these senses for effective navigation. The existing literature predominantly models sensing schemes similar to fields of vision, possibly due to an inherent human bias towards vision. However, there is substantial biological evidence indicating that many species utilize multiple sensory modalities. This work aims to examine the influence of combining sensing modalities on group behavior. We explore the most generalized scenario of three-dimensional motion, a domain that has not been previously used to study combining sensory information. Through numerical simulations, we investigate the combined effects of auditory and visual sensing on group-level behavior, comparing them to the effects of pure vision and audition. The results reveal that composite sensing enables particles to interact with a larger set of neighbors, thereby accessing more information. At relatively low noise intensities, this interaction facilitates the formation of a single, large, highly aligned group within a narrow sensing region--a feature achievable by combining the individual advantages of the auditory and visual sensing mechanisms. The results in 3D are observed to differ from previous 2D studies in several key ways. First, in the visual mode, polarization exhibits a non-monotonic variation with sensing region size, showing an optimal sensing region that maximizes group alignment, a phenomenon not reported in earlier 2D studies. Second, the transition from disorder to order in the visual mode is more discontinuous in 3D, resembling a first-order phase transition, compared to the second-order-like transitions observed with auditory sensing. These differences highlight the distinct dynamics introduced by the 3D configuration in both visual and auditory modalities. The findings of this study highlight the significant role that integrating information from multiple sensory modalities plays in emergent group-level behavior. These insights could have important applications in both biological and robotic swarms. Building this model solely on sensory information aligns with real systems, where coordinated motion often involves adaptive behaviors and maneuvers [54]. While this model is inspired by sensing mechanisms observed in natural systems, the phase transitions identified are reminiscent of those found in the collective motion of animals, such as fish schools and pigeon flocks [54, 61, 62, 63, 64, 65, 66, 67, 68]. The metrics observed from integrating multiple sensory modalities may be analogous to real biological systems, where sensory fusion supports critical survival functions like foraging and navigation. By enabling rapid phase transitions in coordinated group movements and fostering robust interactions within groups, sensory fusion reduces energy expenditure during communication and enhances the efficiency of collective behaviors [42, 43, 69, 70, 71, 72]. In future work, we aim to extend the model to incorporate heterogeneity in agent properties, such as variations in noise levels, sensing radii, and sensory modalities. These extensions would align the model more closely with real-world systems, where individuals often possess differing sensory capabilities. For instance, agents with reduced sensing abilities may lag in alignment or cohesion, potentially leading to group fragmentation or sub-group formation. Similarly, heterogeneous noise distributions could alter the critical thresholds for phase transitions, introducing more complex dynamics. Exploring these aspects would provide deeper insights into the robustness and adaptability of collective systems under more realistic conditions. Such studies could also help bridge the gap between idealized models and empirical observations in biological systems. **Author Contributions:** The following outlines the contributions of each author. Conceptualization, S.R. ; software, P.R. ; validation, P.R. and S.R.