da Silveira Pedro M M, Fontanari José F
Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil.
Math Biosci. 2024 Sep;375:109245. doi: 10.1016/j.mbs.2024.109245. Epub 2024 Jul 3.
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.
同步是集体行为中最显著的实例之一，出现在许多自然现象中。例如，在某些蚂蚁物种中，蚂蚁大部分时间在巢穴内不活动，但它们的活动爆发高度同步，且涉及整个巢穴群体。在这里，我们重新审视一个模拟模型，该模型通过自催化行为产生这种同步的节律活动，即活跃的蚂蚁可以激活不活跃的蚂蚁，随后是一段休息期。我们推导了一组延迟微分方程，这些方程为大型蚁群的模拟提供了准确描述。对定点解的分析，辅以方程的数值积分，表明当休息期大于阈值且不活跃蚂蚁自发激活的情况非常不可能发生时，存在稳定的极限环解，因此大多数蚂蚁的唤醒是由活跃蚂蚁完成的。此外，我们认为在有限规模蚁群的模拟中观察到的持续振荡是由于种群统计噪声的共振放大。
