This work is concerned with the fast–slow dynamics for intraguild predation models with evolutionary effects. Assuming the survival pressure of the weaker predator induces evolution of it to the intraguild predator, then the system can be viewed as a singularly perturbed problem with two different time scales—predation time scale and evolution time scale. Using the geometric singular perturbation theory, we first completely analyze the limiting slow–fast dynamics of the system which involve the existence of turning points. Then, an application of the geometric singular perturbation theory gives rise to the birth of relaxation oscillations caused by the turning points and the associated delay of stability loss. From our main results, one can see that evolution enhances survival rates of inferior competitors.

中文翻译：

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具有进化效应的行内捕食模型的快慢动力学

这项工作涉及具有进化效应的行会内捕食模型的快慢动力学。假设较弱的捕食者的生存压力促使其进化为公会内的捕食者，那么该系统可以看作是一个具有两个不同时标的奇异摄动问题-捕食时标和进化时标。使用几何奇异摄动理论，我们首先完全分析系统的有限慢速-快速动力学，其中涉及转折点的存在。然后，几何奇异摄动理论的应用引起了由转折点和相关的稳定性损失引起的弛豫振荡的产生。从我们的主要结果中可以看出，进化提高了劣等竞争对手的生存率。