Department of Physics, American University of Beirut, Riad El-Solh 1107, 2020, Beirut, Lebanon.
National Center for Remote Sensing, CNRS-L, Riad El Solh 1107, 2260, Beirut, Lebanon.
Sci Rep. 2019 Feb 8;9(1):1699. doi: 10.1038/s41598-018-37457-y.
Experiments with groups of fish inside a circular tank have provided valuable insights into the nature of leadership in social groups. Sophisticated mathematical models were constructed with a view to recovering observed schooling and leadership behavior in such experiments. Here, and with the help of variations on a promising class of such models, we explore a dual set of social concerns, namely the likelihood of permanent evasion from a cohesive group by a controlled individual in confinement. Our minimal model reduces to a leader-follower configuration, with cone-of-vision driven interactions inside a circular domain. We show that the resulting dynamical system sustains a rich supply of non-aligned, straying "follower" states, the dynamics on which displays (chaotic) intermittency between boundary following behavior and infrequent long flights. We map these states in configuration space and explore transitions between them. We demonstrate robustness of observed behavior by considering model variations, as well as alternate leader control trajectory. While it is too early to draw the implications of leader-follower dynamics to collective behavior, we do confirm that a model stray fish relates to a self-organized school bouncing back and forth along the diameter very much like a follower responds to a point leader in our model. We further draw the implications of our results to the study of dynamical systems with discontinuities, robotics, and the study of human behavior in the face of normative control and confinement.
在圆形水箱中的鱼类群体实验为研究社会群体中的领导本质提供了有价值的见解。构建了复杂的数学模型，以期从这些实验中恢复观察到的群体游动和领导行为。在这里，借助于一类有前途的模型的变体，我们探讨了双重的社会关注点，即个体在受限环境中是否可能永久逃避有凝聚力的群体。我们的最简模型简化为一个领导者-跟随者配置，在圆形区域内通过视觉圆锥进行交互。我们表明，由此产生的动力系统维持了大量非对齐的、偏离的“跟随者”状态，其动力学表现为边界跟随行为和罕见的长距离飞行之间的（混沌）间歇性。我们在配置空间中对这些状态进行映射，并探索它们之间的转变。我们通过考虑模型变体以及替代的领导者控制轨迹来证明所观察到的行为的稳健性。虽然现在还为时尚早，无法将领导者-跟随者动态的含义推断到集体行为中，但我们确实证实，模型中的“流浪鱼”与自组织的鱼群非常相似，后者沿着直径来回反弹，就像跟随者对模型中的一个点状领导者的反应一样。我们进一步将我们的结果与不连续动力系统、机器人技术以及在规范性控制和限制面前的人类行为研究联系起来。
