勷勤数学•专家报告

题      目：Global competitive dynamics of Aedes aegypti and Aedes albopictus

报  告  人：郑波  教授  (邀请人：丁维维)

                                  广州大学

时      间：10月21日  10：00-11：00

地     点：学院阶梯二楼报告厅

报告人简介:

       郑波，博士，教授，博士生导师。主要从事常微分方程、泛函微分方程及生物数学模型的理论与应用研究，在《Nature》、《SIAM Journal of Applied Mathematics》、《Journal of Mathematical Biology》、《中国科学》、《Journal of Differential Equations》、《Journal of Dynamics and Differential Equations》、《Journal of Theoretical Biology》、《Theoretical Population Biology》等国际国内重要刊物上发表论文40余篇。先后主持国家自然科学基金4项、广州市教育局3项，2014年入选广东省高校优秀青年教师培育对象，是教育部创新团队“泛函微分方程及相关问题”的骨干成员。获得首届秦元勋青年数学奖。

摘      要：

       This talk is concerned with the global competitive dynamics of Aedes aegypti and Aedes albopictus. We develop a planar time-switched model that considers favorable-unfavorable seasonal shifts, the interspecific mating competition in the favorable season, and the overwintering capacity in the unfavorable season. During the favorable season, we find a sharp estimation of a separatrix that determines the fate of Aedes aegypti and Aedes albopictus. When the two species undergo seasonal transition, the separatrix disappears and the time switching results in the discontinuity of the vector field, which causes complex dynamical behaviors. By analyzing the associated Poincare map, we obtain sufficient and/or necessary conditions for the existence and stability of periodic solutions. The results show that asymmetric mating interference and wintering ability in suitable seasons were important factors affecting the interaction dynamics of Aedes aegypti and Aedes albopictus. By understanding and potentially manipulating these interactions, it might be possible to effectively reduce the size of unwanted species. This is a joint work with Professor Jianshe Yu, Dr Hongpeng Guo and my PhD student Lijie Chang.

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