This paper is concerned with the attracting set of an ant colonies model with bounded noisy perturbation. This perturbation is modeled by the well-known Ornstein–Uhlenbeck process and the arc tangent function. For the random model, we first verify the existence and uniqueness of the global positive solution, and then prove the existence of the deterministic attracting set. Furthermore, in order to reveal more detailed information about the long-time behavior of the ant colonies system, we analyze the internal structure of the attracting set and provide some conditions under which coexistence (or extinction) of the ant species exists in the ant colonies system.

中文翻译：

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随机蚁群模型确定性吸引集的存在性及内部结构

本文研究的是有界噪声扰动的蚁群模型的吸引集。这种扰动由著名的 Ornstein-Uhlenbeck 过程和反正切函数建模。对于随机模型，我们首先验证全局正解的存在性和唯一性，然后证明确定性吸引集的存在性。此外，为了揭示有关蚁群系统长期行为的更详细信息，我们分析了吸引集的内部结构，并提供了蚁群中蚂蚁物种共存（或灭绝）的一些条件系统。