We guide the reader on a journey through mathematical modeling and numerical analysis, emphasizing the crucial interplay of both disciplines. Targeting undergraduate students with basic knowledge in dynamical systems and numerical methods for ordinary differential equations, we explore a model from mathematical biology where numerical methods fail badly due to catastrophic floating point errors. We analyze the reasons for this behavior by studying the steady states of the model and use the theory of invariants to develop an alternative model that is suited for numerical simulations. Our story intends to motivate combining analytical and numerical knowledge, even in cases where the world looks fine at first sight. We have set up an online repository containing an interactive notebook with all numerical experiments to make this study fully reproducible and useful for classroom teaching.

翻译：我们引导读者踏上一段数学建模与数值分析的探索之旅，强调这两个学科的关键相互作用。针对具备常微分方程动力系统及数值方法基础知识的本科生，我们研究了一个数学生物学模型，在该模型中，数值方法因灾难性浮点误差而严重失效。我们通过分析模型的稳态来探究这一行为的原因，并利用不变量理论开发了一个适用于数值模拟的替代模型。我们的叙述旨在激励读者结合解析与数值知识，即使在最初看似一切正常的情况下也是如此。我们建立了一个在线资源库，其中包含一个交互式笔记本和所有数值实验，以确保这项研究可完全复现，并适用于课堂教学。