Abstract：
Synchronization is one of the most striking instances of collective behavior, occurring in many natural phenomena. For example, in some ant species, ants are inactive within the nest most of the time, but their bursts of activity are highly synchronized and involve the entire nest population. Here we revisit a simulation model that generates this synchronized rhythmic activity through autocatalytic behavior, i.e., active ants can activate inactive ants, followed by a period of rest. We derive a set of delay differential equations that provide an accurate description of the simulations for large ant colonies. Analysis of the fixed-point solutions, complemented by numerical integration of the equations, indicates the existence of stable limit-cycle solutions when the rest period is greater than a threshold and the event of spontaneous activation of inactive ants is very unlikely, so that most of the arousal of ants is done by active ants. Furthermore, we argue that the persistent oscillations observed in the simulations for colonies of finite size are due to resonant amplification of demographic noise.
摘要：
同步是集体行为最引人注目的例子之一，发生在许多自然现象中。例如,在一些蚂蚁物种中，蚂蚁大部分时间在巢内是不活跃的，但是它们的活动爆发是高度同步的，涉及整个巢穴种群。在这里，我们重新审视一个模拟模型，该模型通过自动催化行为产生这种同步的节奏活动，即，活跃的蚂蚁可以激活不活跃的蚂蚁，接下来是一段时间的休息。我们推导了一组延迟微分方程，这些方程可以准确描述大型蚁群的模拟。分析定点解决方案，辅以方程的数值积分，表明当休息期大于阈值并且不活跃蚂蚁的自发激活事件非常不可能时，存在稳定的极限循环解，所以蚂蚁的大部分唤醒是由活跃的蚂蚁完成的。此外，我们认为，在有限大小的菌落模拟中观察到的持续振荡是由于人口噪声的共振放大。
