论文标题
在经性捕食者和专业捕食者竞争的三倍尺度模型中的复杂振荡模式
Complex oscillatory patterns in a three-timescale model of a generalist predator and a specialist predator competing for a common prey
论文作者
论文摘要
在本文中，我们开发和分析了一个模型，该模型研究了专家捕食者，通才捕食者及其在具有三个时间尺度的两次周期生态系统中的共同猎物之间的相互作用。我们假设猎物在更快的时间范围内运行，而专家和通才捕食者分别在缓慢和超级阶段的时间表上运作。将通才捕食者的捕食效率视为主要的参数，以及研究的猎物物种形成的饮食比例作为次要参数，我们获得了许多丰富而有趣的动态，包括放松振荡，混合模式振荡（MMOS），近临界椭圆形的椭圆形爆发模式，torus torus torus torus torus torus torus torus torus torus torus torus torus causards and-can can can can can can can can can torus can can can can。通过将时间表分为两个类，并使用类之间的时间尺度分离，我们将应用一快的/两戳和两快的/一句慢分析技术来获得有关动力学的见解。利用单个子系统的几何特性和流量，结合了整个系统的分叉分析和数值延续，我们对振荡动力学进行了分类，并讨论了从一种动力学到另一种动力学的过渡。在该模型中观察到的振荡模式的类型是在以三个时间表为特征的种群模型中新颖的。其中一些定性类似于小型哺乳动物和昆虫的天然周期。此外，振荡动力学表现出圆环乳清，混合型圆环牛排和MMO，在自我交流的关键歧管的一个不变板附近延迟稳定损失，然后在三频段型模型中没有被吸引到关键流派的邻近吸引人的片段。
In this paper, we develop and analyze a model that studies the interaction between a specialist predator, a generalist predator, and their common prey in a two-trophic ecosystem featuring three timescales. We assume that the prey operates on a faster timescale, while the specialist and generalist predators operate on slow and superslow timescales respectively. Treating the predation efficiency of the generalist predator as the primary varying parameter and the proportion of its diet formed by the prey species under study as the secondary parameter, we obtain a host of rich and interesting dynamics, including relaxation oscillations, mixed-mode oscillations (MMOs), subcritical elliptic bursting patterns, torus canards, and mixed-type torus canards. By grouping the timescales into two classes and using the timescale separation between classes, we apply one-fast/two-slow and two-fast/one-slow analysis techniques to gain insights about the dynamics. Using the geometric properties and flows of the singular subsystems, in combination with bifurcation analysis and numerical continuation of the full system, we classify the oscillatory dynamics and discuss the transitions from one type of dynamics to the other. The types of oscillatory patterns observed in this model are novel in population models featuring three-timescales; some of which qualitatively resemble natural cycles in small mammals and insects. Furthermore, oscillatory dynamics displaying torus canards, mixed-type torus canards, and MMOs experiencing a delayed loss of stability near one of the invariant sheets of the self-intersecting critical manifold before getting attracted to the adjacent attracting sheet of the critical manifold have not been previously reported in three-timescale models.
