标题： 噪声诱导的群游鱼集体记忆 显示英文标题

标题： Noise-Induced Collective Memory in Schooling Fish

摘要： 成群的鱼常常自我组织成各种集体模式，从极化的鱼群到旋转的磨盘式运动。 数学模型支持这些大尺度模式的出现，这是在没有个体记忆和群体领导的情况下，由局部去中心化的相互作用产生的。 在一个流行的模型中，个体鱼遵循回避、对齐和吸引的规则进行局部交互，群体表现出集体记忆：个体行为的变化会导致依赖于群体过去配置的涌现模式。 然而，驱动这种集体记忆的机制仍然不清晰。 在这里，我们结合数值模拟和分岔理论的工具，发现该模型中从磨盘式运动到鱼群运动的转变是由一个噪声的交叉分岔驱动的，其中两种集体状态相交并交换稳定性。 我们进一步表明，群体动力学的关键特征——分岔特性、瞬时磨盘式运动和集体记忆——可以通过群体极化的现象学模型来捕捉。 我们的研究结果表明，集体记忆来源于噪声分岔，而不是结构双稳性，从而解决了关于其起源的长期模糊问题，并为鱼类鱼群的普遍模型中的集体相变提供了基本的理解。 显示英文摘要

摘要： Schooling fish often self-organize into a variety of collective patterns, from polarized schooling to rotational milling. Mathematical models support the emergence of these large-scale patterns from local decentralized interactions, in the absence of individual memory and group leadership. In a popular model where individual fish interact locally following rules of avoidance, alignment, and attraction, the group exhibits collective memory: changes in individual behavior lead to emergent patterns that depend on the group's past configurations. However, the mechanisms driving this collective memory remain obscure. Here, we combine numerical simulations with tools from bifurcation theory to uncover that the transition from milling to schooling in this model is driven by a noisy transcritical bifurcation where the two collective states intersect and exchange stability. We further show that key features of the group dynamics - the bifurcation character, transient milling, and collective memory - can be captured by a phenomenological model of the group polarization. Our findings demonstrate that collective memory arises from a noisy bifurcation rather than from structural bistability, thus resolving a long-standing ambiguity about its origins and contributing fundamental understanding to collective phase transitions in a prevalent model of fish schooling.