论文标题
延迟Vicsek模型中的信号传播和线性响应
Signal propagation and linear response in the delay Vicsek model
论文作者
论文摘要
感觉和动作之间的迟钝是一种固有的生物学特征。在这里，我们在Vicsek模型中研究其效果，该模型是一种范式群模型。我们发现：（i）定向相互作用的离散时间延迟会降低强烈比对群跟随领导者的能力，作为回报，增加了它们在随机取向波动上的稳定性； （ii）较长的延迟和更高的速度偏爱弹道，而不是通过群的信息扩散（方向）； （iii）对于短延迟，总方向（顺序参数）的平均变化在领导者的小取向偏置中线性缩放，并在延迟时间内成反比，而其方差首先增加，然后随着延迟的增加而饱和； （iv）当方向保护破裂时，线性响应分解。
Retardation between sensation and action is an inherent biological trait. Here we study its effect in the Vicsek model, which is a paradigmatic swarm model. We find that: (i) a discrete time delay in the orientational interactions diminishes the ability of strongly aligned swarms to follow a leader and, in return, increases their stability against random orientation fluctuations; (ii) both longer delays and higher speeds favor ballistic over diffusive spreading of information (orientation) through the swarm; (iii) for short delays, the mean change in the total orientation (the order parameter) scales linearly in a small orientational bias of the leaders and inversely in the delay time, while its variance first increases and then saturates with increasing delays; (iv) the linear response breaks down when orientation conservation is broken.
