# The Role of Sensory Cues in Collective Dynamics: A Study of Three-Dimensional Vicsek Models
## 1 Introduction
Under sensory constraints, the ability of individuals to gather information from nearby neighbors is limited, as the number of perceivable neighbors decreases. In such cases, the fusion of multiple sensory modalities can provide a significant advantage by compensating for the limitations of any single modality. For example, while many species exhibit a strong preference for a dominant sensing mechanism due to its efficiency--such as bats relying primarily on echolocation--sensory fusion has been shown to enhance spatial and temporal resolution. Specifically, the Egyptian fruit bat (_Rousettus aegyptiacus_) combines visual and echolocation cues to optimize navigation and coordination under varying environmental conditions [42]. This integration of multi-sensory information allows animals to weigh inputs from different modalities and resolve sensory ambiguities, thereby supporting cohesion and alignment within groups [42; 43]. It is evident from these studies that multisensory integration in real-world situations influences group behavior. Improving our understanding of how multimodal sensing impacts group behavior is essential. Previous approaches, such as the graph-theoretic method using consensus and synchronization protocols [44; 45], analyze the impact of multiple sensing modalities, but ignore spatial distribution. The study in [46; 47] introduces a composite model that integrates auditory and visual cues, however, the model is restricted to two dimensions. Extending collective behavior models to three dimensions is crucial because it aligns more closely with the natural environments where these behaviors occur. Many animal groups, such as bird flocks, fish schools, and bat swarms operate in three-dimensional spaces, and their interactions can be significantly different from two-dimensional approximations [48; 49]. The investigation of collective motion in three dimensions has an experimental foundation, with studies tracking the movement of mammalian cells, flying bats, shoaling fish, and swarming mosquitoes or fruit flies [35; 50; 51; 52; 53]. These experimental approaches not only enhance our understanding of the dynamics of the organism, but also provide valuable insights into individual behaviors, including neurological mechanisms [54; 55]. Such findings can inform and inspire the development of computational models for large-scale simulations of three-dimensional collective behavior, enabling rapid testing and analysis of dynamic scenarios. Three-dimensional models provide a better understanding of dynamics and can capture phenomena that are not observable in two-dimensional models, such as complex evasive maneuvers and spatial formations [56; 57]. Therefore, incorporating three-dimensional extensions into collective behavior models is essential to accurately represent and analyze real-world scenarios. Extending collective motion models to three dimensions can be a non-trivial task, as it often depends on the underlying framework. For instance, models that incorporate temporal and spatial derivatives, coupled with biologically inspired sensing mechanisms or interaction potentials, present significant challenges when transitioning to three dimensions while maintaining biological relevance [55; 58]. In contrast, the Vicsek model, due to its minimal assumptions, allows for a straightforward extension to three dimensions, making it an effective tool for studying collective motion [23; 59]. In this paper, we present three collective motion models: one with visual sensing, one with auditory sensing, and a composite model that integrates both auditory and visual sensing, all explored in three dimensions for the first time. We conduct simulations to investigate how these different sensory cues influence the behavior of the group, measured by various order parameters.