标题： 树栖龟蚁觅食动态中的混合反馈振荡 显示英文标题

标题： Mixed-feedback oscillations in the foraging dynamics of arboreal turtle ants

摘要： 我们提出并分析了树栖龟蚁$\textit{Cephalotes goniodontus}$在觅食过程中进出巢穴的动态模型，以探究振荡出现的可能机制。 在我们的模型中，不同行为区域之间的蚂蚁流动与沿途信息素的浓度之间存在混合动态反馈。 一方面，蚂蚁沿着路线沉积信息素，这通过增加返回巢穴的速率提供了正反馈。 另一方面，信息素蒸发是一个负反馈源，因为它会消耗信息素并抑制返回速率。 我们证明了该模型在没有信息素反馈的情况下是全局渐近稳定的。 然后，我们表明，信息素反馈可以通过霍普夫分岔导致平衡点失去稳定性，并引发进出巢穴的流量持续振荡。 这项分析揭示了一种潜在的关键机制，该机制使树栖龟蚁能够有效地优化其路径网络，以最大限度地减少行进路径长度并消除图循环。 显示英文摘要

摘要： We propose and analyze a model for the dynamics of the flow into and out of a nest for the arboreal turtle ant $\textit{Cephalotes goniodontus}$ during foraging to investigate a possible mechanism for the emergence of oscillations. In our model, there is mixed dynamic feedback between the flow of ants between different behavioral compartments and the concentration of pheromone along trails. On one hand, the ants deposit pheromone along the trail, which provides a positive feedback by increasing rates of return to the nest. On the other hand, pheromone evaporation is a source of negative feedback, as it depletes the pheromone and inhibits the return rate. We prove that the model is globally asymptotically stable in the absence of pheromone feedback. Then we show that pheromone feedback can lead to a loss of stability of the equilibrium and onset of sustained oscillations in the flow in and out of the nest via a Hopf bifurcation. This analysis sheds light on a potential key mechanism that enables arboreal turtle ants to effectively optimize their trail networks to minimize traveled path lengths and eliminate graph cycles.