发表机构
Université Paris-Saclay and Université de Paris-Cité, CNRS/IN2P3, IJCLab; Graduate School of Mathematical Sciences, the University of Tokyo（巴黎萨克雷大学和巴黎 Cité 大学，CNRS/IN2P3，IJCLab; 东京大学大学院数理科学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究扩展HANDY模型，纳入不可再生资源和社会效应，通过四微分方程系统分析稳定均衡条件，发现永久环境破坏导致人口崩溃，而可恢复能力与及时干预可避免灭绝。
AI 中文摘要
我们提出了单种群人类与自然动力学（HANDY）模型的一个扩展，该扩展明确纳入了不可再生资源和社会效应。该模型被表述为一个由四个微分方程组成的系统，并为其提供了忠实的离散积分器。在模型中，资源开采与转化通过现实的Holling型功能响应来描述，该响应捕捉了可再生和不可再生资源的饱和效应，同时引入效率损失以描述固有浪费。我们推导了模型参数的解析条件，这些条件确保在人口增长和资源耗竭的情况下仍能实现稳定（且可持续）的均衡。分析中出现的不同动力学情景以及导致这些情景的参数条件，通过广泛的数值模拟加以说明。我们研究的社会效应包括可调节的资源开采和消费速率，以及由人口驱动的自然及其再生能力的退化。一个直接的结论是，永久性环境破坏不可避免地会引发人口崩溃。相反，我们也表明，即使延迟的可恢复能力也可能带来长期生存，并且及时的后期干预往往能完全避免灭绝。
英文摘要
We present an extension of the single-population Human and Nature Dynamics (HANDY) model that explicitly incorporates non-renewable resources and societal effects. The model is formulated as a system of four differential equations for which we provide a faithful discrete integrator. In the model, resource extraction and conversion is described by realistic Holling-type functional responses that capture saturation effects for both renewable and non-renewable resources, while efficiency losses are introduced to describe inherent waste. We derive analytic conditions on the model parameters, needed to ensure stable (and sustainable) equilibria, despite population growth and depletion of resources. The different dynamical scenarios that appear in this analysis and the parametric conditions that lead to them, are illustrated by extensive numerical simulations. The societal effects we investigate include adjustable extraction and consumption rates of the resources, alongside a population-driven degradation of Nature and of its regenerative capacity. One immediate conclusion is that permanent environmental damage inevitably precipitates population collapse. In contrast, we also show that the possibility of recoverable capacities, even delayed, may lead to long-term survival and that timely late-stage interventions often succeed in averting extinction entirely.
Comments24 pages, 15 figures
