Bifurcation Theory and Abrupt Climate Change

分岔理论与气候突变

• 批准号: RGPIN-2020-05009
• 负责人: Langford, William
• 金额: $ 1.53万
• 依托单位: University of Guelph
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759032
• 关键词: Bifurcation; Theory; Abrupt; Climate; Change

In the study of systems of mathematical equations, Bifurcation Theory deals with cases in which small changes in the parameters of the system can lead to qualitative (i.e. topological) changes in the solutions of the equations. Bifurcation Theory tells us that this "cause and effect" relationship can be highly nonlinear, but typically will occur only in a few generic ways, called bifurcations, which mathematicians are beginning to understand very well. In the present work, the equations under study are systems of nonlinear differential equations; that is, equations that determine how a system evolves with time. Equations of this kind are widely used in science, and help in the understanding of many kinds of real systems, for example in physics, engineering, biology and climate.      This research program has two objectives. In the field of mathematics, it will contribute to the advancement of Bifurcation Theory itself, by adding new types of bifurcations to the knowledge base. Outside of mathematics, this research program will extend the application of ideas of Bifurcation Theory to real-world systems, with the goal of better understanding how these systems are likely to change. Some examples of systems that have been investigated from this perspective are: global climate change, patterns of vibrations in mechanical systems, onset of certain cardio-respiratory diseases in humans, and sustainable biodiversity in ecology.      Of all these applications, climate change is selected as the first priority for this research proposal. Very recently, coworkers and I have established that bifurcations may occur in the Earth's climate system, and actually have occurred in climates of the distant past. A preliminary analysis has concluded that a bifurcation to a dramatically warmer climate state awaits us in the future, unless anthropogenic forcing, caused by increased carbon dioxide production, is severely curtailed. This result adds mathematical rigour and gravitas to the dire predictions that have been issued by the Intergovernmental Panel on Climate Change. Further investigations of this catastrophic bifurcation and its mitigation are proposed, using a hierarchy of more sophisticated climate models.

在数学方程系统的研究中，分岔理论处理系统参数的微小变化可能导致方程解的质的（即拓扑）变化的情况。分岔理论告诉我们，这种“因果”关系可能是高度非线性的，但通常只会以几种称为分岔的通用方式发生，数学家们已经开始很好地理解这种方式。在本工作中，所研究的方程是非线性微分方程组；也就是说，确定系统如何随时间演化的方程。此类方程广泛应用于科学领域，有助于理解多种真实系统，例如物理、工程、生物学和气候领域。      该研究计划有两个目标。在数学领域，它将通过向知识库添加新类型的分岔来促进分岔理论本身的进步。在数学之外，该研究项目将把分岔理论的思想应用到现实世界的系统中，目的是更好地理解这些系统可能如何变化。从这个角度研究的系统的一些例子包括：全球气候变化、机械系统的振动模式、人类某些心肺疾病的发作以及生态学中的可持续生物多样性。      在所有这些应用中，气候变化被选为本研究提案的首要任务。最近，我和同事们已经确定，地球气候系统中可能会出现分岔，而且实际上在遥远的过去的气候中就已经发生过分岔。初步分析得出的结论是，除非严重限制二氧化碳产量增加引起的人为强迫，否则未来我们将面临急剧变暖的气候状态。这一结果为政府间气候变化专门委员会发布的可怕预测增添了数学上的严谨性和严肃性。建议使用更复杂的气候模型层次结构对这种灾难性分岔及其缓解措施进行进一步研究。