发表机构
University of Edinburgh; Heriot-Watt University（爱丁堡大学; 赫瑞-瓦特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对现有捕食-食饵模型的缺陷，构建含强阿利效应的极简快慢型模型，结合GSPT分析其R-tipping机制，推导临界速率表达式，明确其为R-tipping极简模型的三个核心要素。
AI 中文摘要
生态建模中的速率诱导突变（R-tipping）的特征是环境参数变化过快，导致种群崩溃且未跨越任何分岔（B-tipping）。一个已知的观测到R-tipping的快慢型捕食-食饵模型[Vanselow、Wieczorek、Feudel，《理论生物学杂志》，479卷，64-72页（2019）]存在非生态的“复苏”问题，即被驱赶到功能性灭绝的种群会恢复至稳定共存状态。我们提出了一个解析上易处理的模型，在快慢型Lotka-Volterra类捕食-食饵系统的食饵动态中引入强阿利效应，该效应会引发双稳态，从而使灭绝状态成为真正的吸引子。应用几何奇异摄动理论（GSPT），我们描述了通过“斜坡式”调整食饵环境容纳量的倒数得到的扩展模型的动态。我们证明存在一个抛物线形的折叠临界流形，其具有折叠鞍奇点，该奇点的强鸭解将追踪移动共存状态的解与突变至灭绝的解分隔开。模型的解析简单性使我们能够推导区分“追踪”与“突变”动态的临界速率的显式表达式。最后，我们指出我们的系统代表了速率诱导灭绝突变的极简模型，因为它包含三个关键要素：双稳态、折叠临界流形和折叠鞍型鸭解。
英文摘要
Rate-induced tipping ("R-tipping") in ecological modelling is characterised by too-rapid change of an environmental parameter causing collapse of a population without any bifurcation being crossed ("B-tipping"). A well-known example of a slow-fast predator-prey model in which R-tipping is observed [Vanselow, Wieczorek, Feudel, Journal of Theoretical Biology, 479, 64-72 (2019)] suffers from unecological "resurgence", whereby populations driven to functional extinction recover towards stable coexistence. We propose an analytically tractable model, incorporating a strong Allee effect into the prey dynamics in a slow-fast Lotka-Volterra-type predator-prey system, which induces bistability and thus renders the extinction state a genuine attractor. Applying geometric singular perturbation theory (GSPT), we describe the dynamics of the extended model that is obtained by "ramping" of the inverse prey carrying capacity. We show the presence of a parabolic-shaped, folded critical manifold which admits a folded saddle singularity, the strong canard of which separates solutions that track the moving coexistence state from those that tip to extinction. The analytical simplicity of our model allows us to derive explicit expressions for the critical rate that separates "tracking" from "tipping" dynamics. Finally, we argue that our system represents a minimal model for rate-induced tipping to extinction, in that it incorporates three essential ingredients: bistability, a folded critical manifold, and a folded-saddle-type canard.
