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: 261353-2013
• 负责人: Zhu, Huaiping
• 金额: $ 1.68万
• 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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635319
• 关键词: Bifurcation; Theory; Applications; Mathematical; Biology

My research area includes bifurcation theory and Hilbert's 16th problem for quadratic vector fields and application in mathematical biology. We hope to prove the finiteness part of the sweet Hilbert's 16th problem for quadratic vector fields, namely, to prove that there exists a natural number N such that any quadratic vector field in the plane has at most N limit cycles. I expect to prove that all the graphics with nilpotent point of elliptic or saddle type, degenerate graphics have finite cyclicity.West Nile virus, and other emerging and reemerging vector-borne diseaes are causing concerns to government, health officials and the public. By this study we will understand how the climate change has the impact on vector abundance and spreading of the diseases. This research will enable to create the early warning systems for prediction and control of vector-borne diseases in Canada.

主要研究方向为二次向量场的分支理论、希尔伯特第16问题及其在数学生物学中的应用。我们希望证明二次向量场的希尔伯特第16问题的有限性部分，即证明存在一个自然数N，使得平面上的任何二次向量场至多有N个极限环。我期望证明所有具有幂零点的椭圆型或鞍型图，退化图都有有限圈性。西尼罗河病毒和其他新出现和重新出现的病媒传播疾病引起了政府，卫生官员和公众的关注。通过这项研究，我们将了解气候变化如何对病媒丰度和疾病传播产生影响。这项研究将有助于建立早期预警系统，以预测和控制加拿大的病媒传播疾病。