Rate-Induced Tipping In NonAutonomous Systems

该项目旨在为复杂系统的关键转变研究做出重要贡献。特别是，它解决了具有非自治动力学和应用于气候的系统的速率诱导引爆现象。研究工作将侧重于识别产生关键转变的数学机制，并在非自治分岔理论的背景下对其进行分类，并测试所得理论对非自治气候模型的有效性，这些模型无法用最先进的数学工具进行处理。申请人在该主题上的开创性成果，他的跨学科背景和对非自主动力系统理论的贡献，加上在主办机构对随机和集值动力系统的计划培训，以及导师在该领域世界领先的专业知识的支持，使他处于一个独特的位置，可以有效地接受挑战。研究人员还将巩固他在确定性非自治动力学和分岔理论方面的专业知识，并将其与随机和集值动力系统的新技能相补充。因此，在非自主动力系统领域获得了高度竞争的形象。另一方面，他将把他在卡拉萨姆齐微分方程和费率诱导小费方面的专业知识带到主办机构，并通过与巴利亚多利德大学和慕尼黑工业大学的合作，为伦敦帝国理工学院庞大的国际研究网络做出贡献。最后，该行动的长期影响包括跨学科的关键部门，如调查温室气体排放增长对地球自然时间强迫（因此非自主）气候的影响。

This project aims at making crucial contributions to the study of critical transitions for complex systems. In particular, it addresses the phenomenon of rate-induced tipping for systems with nonautonomous dynamics and applications to climate. The research efforts will focus on identifying the mathematical mechanisms generating the critical transition classifying them in the context of nonautonomous bifurcation theory, and testing the efficacy of the resulting theory on non-autonomous climate models which are not treatable with the state-of-the-art mathematical tools. The applicant's pioneering results on the subject, his interdisciplinary background and contributions to the theory of non-autonomous dynamical systems together with the planned training in random and set-valued dynamical systems at the host institution and the support of the supervisor's world-leading expertise in the field put him in a unique position to effectively take on the challenge. The researcher will also consolidate his expertise in deterministic nonautonomous dynamics and bifurcation theory and complement it with new skills in random and set-valued dynamical systems. Thus, obtaining a highly competitive profile in the field of nonautonomous dynamical systems. On the other hand, he will bring his expertise on Carathéodory differential equations and rate-induced tipping to the host institution and, by mean of his collaborations with the University of Valladolid and Technical University Munich, contribute to the big international research network at Imperial College London. Finally the long-term impact of the action includes interdisciplinary key sectors like the investigation of the effect of the growth of emissions of greenhouse gasses on the naturally time-forced (thus nonautonomous) climate of the planet.