Transients in ecology are extremely important since they determine how equilibria are approached. The debate on the dynamic stability of ecosystems has been largely focused on equilibrium states. However, since ecosystems are constantly changing due to climate conditions or to perturbations driven by the climate crisis or anthropogenic actions (habitat destruction, deforestation, or defaunation), it is important to study how dynamics can proceed till equilibria. This article investigates the dynamics and transient phenomena in small food chains using mathematical models. We are interested in the impact of habitat loss in ecosystems with vegetation undergoing facilitation. We provide a dynamical study of a small food chain system given by three trophic levels: primary producers, i.e., vegetation, herbivores, and predators. Our models reveal how habitat loss pushes vegetation towards tipping points, how the presence of herbivores in small habitats could promote ecosystem’s extinction (ecological meltdown), or how the loss of predators produce a cascade effect (trophic downgrading). Mathematically, these systems exhibit many of the possible local bifurcations: saddle-node, transcritical, Andronov–Hopf, together with a global bifurcation given by a heteroclinic bifurcation. The associated transients are discussed, from the ghost dynamics to the critical slowing down tied to the local and global bifurcations. Our work highlights how the increase of ecological complexity (trophic levels) can imply more complex transitions. This article shows how the pernicious effects of perturbations (i.e., habitat loss or hunting pressure) on ecosystems could not be immediate, producing extinction delays. These theoretical results suggest the possibility that some ecosystems could be currently trapped into the (extinction) ghost of their stable past.

生态学中的瞬态非常重要，因为它们决定了如何接近平衡。关于生态系统动态稳定性的争论主要集中在平衡状态。然而，由于气候条件或气候危机或人为行为（栖息地破坏、森林砍伐或动物区系丧失）引起的扰动导致生态系统不断变化，因此研究动态如何进行直至达到平衡非常重要。本文使用数学模型研究小型食物链中的动态和瞬态现象。我们感兴趣的是生态系统中栖息地丧失对植被促进作用的影响。我们提供了一个由三个营养级别给出的小型食物链系统的动态研究：初级生产者，即植被、食草动物和捕食者。我们的模型揭示了栖息地丧失如何将植被推向临界点，小型栖息地中食草动物的存在如何促进生态系统的灭绝（生态崩溃），或者捕食者的丧失如何产生级联效应（营养降级）。在数学上，这些系统表现出许多可能的局部分叉：鞍节点、跨临界、Andronov-Hopf，以及由异宿分叉给出的全局分叉。讨论了相关的瞬态，从鬼动力学到与局部和全局分叉相关的临界减速。我们的工作强调了生态复杂性（营养级）的增加如何意味着更复杂的转变。这篇文章展示了扰动（即栖息地丧失或狩猎压力）对生态系统的有害影响是如何无法立即产生的，产生灭绝延迟。这些理论结果表明，某些生态系统目前可能陷入其稳定过去的（灭绝）幽灵中。