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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=717493
• 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.

在数学方程式系统的研究中，分叉理论涉及系统参数的小变化可以导致方程解决方案解决方案的定性（即拓扑）变化。分叉理论告诉我们，这种“因果关系”的关系可能是高度非线性的，但通常只会以几种通用方式发生，即数学家开始很好地理解这些关系。在目前的工作中，所研究的方程是非线性微分方程的系统。也就是说，确定系统如何随时间发展的方程式。这种方程式在科学中广泛使用，并有助于理解许多实际系统，例如物理，工程，生物学和气候。 该研究计划有两个目标。在数学领域，它将通过在知识库中添加新类型的分叉方式来促进分叉理论本身的发展。在数学外，该研究计划将将分叉理论的思想的应用扩展到现实世界系统，以便更好地了解这些系统可能如何改变。从这个角度进行了研究的一些示例是：全球气候变化，机械系统中的振动模式，人类某些心脏呼吸系统疾病的发作以及生态学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建议的首要任务。最近，我和同事确定，分叉可能发生在地球的气候系统中，并且实际上发生在遥远过去的气候中。初步分析得出的结论是，将来对动态气候状态的分叉等待着我们，除非由二氧化碳产量增加引起的人为强迫会严重削弱。该结果将数学严格和引力增加了，政府间小组对气候变化发出的方向预测。使用更复杂的攀岩模型的层次结构提出了对这种灾难性分叉及其缓解措施的进一步研究。