College of Music, Florida State University, Tallahassee, FL, 32306, USA.
Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA.
J Math Biol. 2024 Sep 12;89(4):41. doi: 10.1007/s00285-024-02136-2.
Foraging for resources is an essential process for the daily life of an ant colony. What makes this process so fascinating is the self-organization of ants into trails using chemical pheromone in the absence of direct communication. Here we present a stochastic lattice model that captures essential features of foraging ant dynamics inspired by recent agent-based models while forgoing more detailed interactions that may not be essential to trail formation. Nevertheless, our model's results coincide with those presented in more sophisticated theoretical models and experiments. Furthermore, it captures the phenomenon of multiple trail formation in environments with multiple food sources. This latter phenomenon is not described well by other more detailed models. We complement the stochastic lattice model by describing a macroscopic PDE which captures the basic structure of lattice model. The PDE provides a continuum framework for the first-principle interactions described in the stochastic lattice model and is amenable to analysis. Linear stability analysis of this PDE facilitates a computational study of the impact various parameters impart on trail formation. We also highlight universal features of the modeling framework that may allow this simple formation to be used to study complex systems beyond ants.
觅食是蚁群日常生活的重要过程。蚂蚁在没有直接交流的情况下，利用化学信息素自行组织成路径，这一过程令人着迷。本文提出了一个随机格点模型，该模型受到基于主体的最新模型的启发，捕捉了觅食蚂蚁动力学的基本特征，同时摒弃了可能对路径形成不重要的更详细的相互作用。然而，我们的模型结果与更复杂的理论模型和实验结果一致。此外，它还捕获了在具有多个食物源的环境中形成多条路径的现象。这一现象在其他更详细的模型中无法很好地描述。我们通过描述一个捕获格点模型基本结构的宏观 PDE 来补充随机格点模型。该 PDE 为随机格点模型中描述的基本相互作用提供了一个连续体框架，并且易于分析。该 PDE 的线性稳定性分析促进了对各种参数对路径形成影响的计算研究。我们还强调了建模框架的通用特征，这些特征可能允许使用这种简单的形成来研究超越蚂蚁的复杂系统。
