报告题目:Existence and uniqueness of periodic orbits in a discrete model on Wolbachia infection frequency

报告时间: 2022年6月22日(星期三), 20:50-21:30

报告地点: 腾讯会议 846 210 770

内容摘要: This talk consider a discrete model on Wolbachia infection frequency. In the model, a periodic and impulsive release strategy is assumed, where infected males are released during the first N generations with the release ratio a and the release is terminated from N+1-th generation to T-th generation. We find a release ratio threshold denoted by b and prove the existence of periodic solutions for the model when 0<a<b. For the special case when N=1 and T=2 we prove that the model has a unique periodic solution which is unstable when 0<a<b. While a>b, no periodic phenomenon occurs and the Wolbachia fixation equilibrium is globally asymptotically stable. Numerical simulations are also provided to illustrate our theoretical results. One main contribution of this work is to offer a new method to determine the exact number of periodic orbits to discrete models. However, for the general case, the uniqueness of the periodic solution is still pending. This is a joint work with Prof Jianshe Yu in Guangzhou University.

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30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。

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