The mechanisms through which work is organized are central to understanding how complex systems function. Previous studies suggest that task organization can emerge via nonlinear dynamical processes wherein individuals interact and modify their behavior through simple rules. However, there is very limited theory about how those processes are shaped by behavioral variation within social groups. In this work, we propose an adaptive modeling framework on task allocation by incorporating variation both in task performance and task-related metabolic rates. We study the scaling effects of colony size on the resting probability as well as task allocation. We also numerically explore the effects of stochastic noise on task allocation in social insect colonies. Our theoretical and numerical results show that: (a) changes in colony size can regulate the probability of colony resting and the allocation of tasks, and the direction of regulation depends on the nonlinear metabolic scaling effects of tasks; (b) increased response thresholds may cause colonies to rest in varied patterns such as periodicity. In this case, we observed an interesting bubble phenomenon in the task allocation of social insect colonies for the first time; (c) stochastic noise can cause work activities and task demand to fluctuate within a range, where the amplitude of the fluctuation is positively correlated with the intensity of noise.

组织工作的机制是理解复杂系统如何运作的核心。以前的研究表明，任务组织可以通过非线性动态过程出现，其中个人通过简单的规则进行交互和修改他们的行为。然而，关于这些过程如何由社会群体内的行为变化塑造的理论非常有限。在这项工作中，我们通过结合任务表现和任务相关代谢率的变化，提出了一个任务分配的自适应建模框架。我们研究了菌落大小对静息概率和任务分配的缩放效应。我们还数值探讨了随机噪声对社会昆虫群落任务分配的影响。我们的理论和数值结果表明：(a) 菌落大小的变化可以调节菌落静止的概率和任务的分配，调节的方向取决于任务的非线性代谢缩放效应；(b) 增加的反应阈值可能会导致菌落以不同的模式休息，例如周期性。在这种情况下，我们第一次在社会性昆虫群体的任务分配中观察到了一个有趣的气泡现象；(c) 随机噪声会使工作活动和任务需求在一个范围内波动，波动幅度与噪声强度呈正相关。在这种情况下，我们第一次在社会性昆虫群体的任务分配中观察到了一个有趣的气泡现象；(c) 随机噪声会使工作活动和任务需求在一个范围内波动，波动幅度与噪声强度呈正相关。在这种情况下，我们第一次在社会性昆虫群体的任务分配中观察到了一个有趣的气泡现象；(c) 随机噪声会使工作活动和任务需求在一个范围内波动，波动幅度与噪声强度呈正相关。