AI 中文总结
研究多智能体系统中集体运动与观点动态的关系，提出耦合模型，空间动力学由吸引 - 排斥作用控制，内部动力学用德弗安特型观点模型描述，揭示了置信阈值和吸引强度对观点簇及群体分布的影响，对相关研究有重要意义。
AI 中文摘要
多智能体系统中的集体动力学为理解个体间简单交互如何产生连贯的群体层面模式提供了有力框架。此类现象在许多自然和人工系统中都能观察到。在很多情况下，智能体不仅由其空间运动表征，还由内部状态（如观点或偏好）表征，且这些内部状态会通过与同伴的交互而演变。理解这些内部状态如何影响集体运动以及空间组织如何反过来影响内部动力学仍是一个重要挑战。在这项工作中，我们提出了一个耦合集体运动和观点动态的模型。空间动力学由吸引 - 排斥相互作用控制，而内部动力学由德弗安特型观点模型描述。我们的结果表明，观点动态的置信阈值在控制观点簇数量方面起关键作用，而依赖观点的空间吸引强度决定了这些簇在空间上是合并还是保持分离。此外，对于完全一致状态，我们使用半解析方法推导了使用非线性吸引核时静止群体分布半径的表达式。所提出的框架可能对研究集体决策、动物群体行为和群体机器人中的协调策略有用。
英文摘要
Collective dynamics in multi-agent systems provide a powerful framework for understanding how coherent group-level patterns can emerge from simple interactions between individuals. Such phenomena are observed in many natural and artificial systems, including animal groups, robotic swarms, and distributed decision-making processes. In many situations, agents are not only characterized by their spatial motion, but also by internal states, e.g., opinions or preferences, which evolve through interactions with peers. Understanding how these internal states influence collective motion, and how spatial organization in turn affects internal dynamics, remains an important challenge. In this work, we propose a model of coupled collective motion and opinion dynamics. The spatial dynamics are governed by attraction--repulsion interactions, while the internal dynamics are described by a Deffuant-type opinion model. Our results show that the confidence threshold of the opinion dynamics plays a key role in controlling the number of opinion clusters, whereas the strength of the opinion-dependent spatial attraction determines whether these clusters spatially merge or remain separated. In addition, for the full-consensus state, we derive the expression for the radius of the stationary swarm distribution when a nonlinear attraction kernel is used, using a semi-analytical approach. The proposed framework may be useful for studying collective decision-making, animal group behavior, and coordination strategies in swarm robotics.
