Bifurcation theory and applications in mathematical biology

分岔理论及其在数学生物学中的应用

• 批准号: RGPIN-2018-06520
• 负责人: Zhu, Huaiping
• 金额: $ 2.04万
• 依托单位: York University
• 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=759197
• 关键词: Bifurcation; theory; applications; mathematical; biology

Hilbert's 16th problem is the most difficult one proposed by Hilbert 100 year ago but still challenges our wisdom. Canadian mathematicians have been leading and contributing to the research on the problem. As an excellent mathematician working in this field for over 20 years, the applicant proposed to continue to tackle the finiteness part of the problem by showing that the number of periodic solutions which can be born from a degenerate solution is finite. The proposed research will enable the applicant to maintain the leading and active position in this field. The mathematical knowledge and skills for solving Hilbert's 16th problem can also help to understand the mechanisms and complexity of the ecology of our ecosystems. The applicant will study the birth and death of the fast-slow alternating periodic phenomena in the predator-prey type of systems. Amazingly, such study not only helps the understanding of the biology of predator-prey but also can help to solve Hilbert's 16th problem. Using the similar tools of dynamical systems, the applicant proposes to study the transmission and spread of mosquito-borne diseases, such as West Nile virus. To prepare and respond to emerging mosquito-borne threat, the applicant will build new predictive models to forecast the mosquito-abundance, triggering factors and mechanisms of an outbreak, and reason of recurrence of the outbreak of the mosquito-borne virus. The advanced research based on the monitoring and surveillance program data and real-time forecasting tools development considering climate change will enable us to know early the risk so that people will get prepared and protected from the biting of virus-carrying mosquitoes. The applicant will also consider the factors including daily temperature and rainfall, community and urban variations; wildlife species diversity and distribution. Canadians will for sure benefit directly and indirectly from his research.

希尔伯特（Hilbert）的第16个问题是希尔伯特（Hilbert）100年前提出的最困难的问题，但仍然挑战了我们的智慧。加拿大数学家一直在领导并为有关该问题的研究做出贡献。作为一名出色的数学家在该领域工作了20多年，申请人提议通过表明可以从退化解决方案诞生的周期性解决方案的数量是有限的，以继续解决问题的有限部分。拟议的研究将使申请人能够维持该领域的领先和主动地位。解决希尔伯特第16个问题的数学知识和技能也可以帮助理解生态系统生态学的机制和复杂性。申请人将研究捕食者类型的系统中快速降低的周期性现象的诞生和死亡。令人惊讶的是，此类研究不仅有助于理解捕食者捕食者的生物学，而且可以帮助解决希尔伯特的第16个问题。申请人使用类似的动力学系统工具研究蚊子传播疾病（例如西尼罗河病毒）的传播和传播。为了准备和应对新兴的蚊子 - 传播威胁，申请人将建立新的预测模型，以预测爆发爆发的蚊子充足，触发因素和机制，以及复发蚊子 - 传播病毒爆发的理由。基于监测和监视计划数据以及考虑气候变化的实时预测工具开发的高级研究将使我们能够尽早了解风险，以便人们将做好准备并受到保护，以免咬人病毒的蚊子。申请人还将考虑包括每日温度和降雨，社区和城市变化的因素；野生动植物物种多样性和分布。加拿大人肯定会直接和间接地从他的研究中受益。