报告题目1：Dynamics of Intraguild Predation Models
主讲人：舒洪英教授
时 间：2025年10月31日（周五）14：00
地 点：腾讯会议(458879846)
主办单位：AC米兰中文
主讲人简介：
舒洪英，2010年获哈尔滨工业大学博士学位。2008年在加拿大阿尔伯塔大学留学两年。2011年至2014年先后在加拿大新不伦瑞克大学、加拿大瑞尔森大学和约克大学任AARMS博士后研究员。2014年12月至2025年6月先后在同济大学、陕西师范大学任特聘教授，博士生导师。2025年7月至今任广州大学教授，博士生导师。2016年获上海市浦江人才计划。先后主持2项国家自然科学基金面上项目，1项青年项目，1项上海市自然科学基金项目，1项加拿大科研基金项目。主要研究微分动力系统及其在生物数学上的应用，发表SCI收录论文50余篇，分别发表在 J. Math. Pures Appl., SIAM Journal of Applied Mathematics, Journal of Differential Equations, Nonlinearity, Journal of Dynamics and Differential Equations, Journal of Mathematical Biology, Bulletin of Mathematical Biology 和Journal of Theoretical Biology等SCI期刊上。任美国数学学会MR评论员、欧洲数学学会zbMATH评论员。
摘要:
We incorporate a stage structure characterized by the maturation delay of intraguild (IG) prey into a three-species IG predation (IGP) model. We derive conditions for the existence and stability of nonnegative equilibria. By selecting the IG prey maturation delay as a bifurcation parameter at the positive equilibrium, we perform Hopf bifurcation analysis and obtain stability switch results. Furthermore, we conduct double Hopf bifurcation analysis using the mortality rate of immature IG prey and the maturation delay of IG prey as bifurcation parameters to further categorize the model dynamics near the double Hopf bifurcation points. It is demonstrated that our model exhibits complex dynamic behavior, such as stability switches, the coexistence of multiple stable periodic solutions, and quasi-periodic orbits. Our findings indicate that Hopf bifurcation and double Hopf bifurcation can lead to multiple types of species coexistence: Species coexist at the equilibrium or through sustained oscillations or irregular oscillations.
报告题目2：Periodic dynamics of a single-species population model based on the discrete Beverton-Holt equation
主讲人：郑波教授
时 间：2025年10月31日（周五）15：00
地 点：腾讯会议(458879846)
主办单位：AC米兰中文
主讲人简介：
郑波，博士，教授，博士生导师。主要从事蚊媒传染病数学建模、理论分析及应用的研究，在《Nature》、《SIAM Journal of Applied Mathematics》、《Journal of Mathematical Biology》、《中国科学》、《Journal of Differential Equations》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5项。 2019年获得首届秦元勋青年数学奖，2024年以第一完成人获得广东省自然科学奖二等奖。
摘要:
We are first concerned with the discrete Beverton-Holt equation, where the coefficients are two positive periodic sequences. We find a sufficient condition that ensures if the origin is unstable, there exists a unique positive periodic solution that globally attracts all positive solutions. This confirms the Cushing-Henson conjecture (a) under weaker conditions. A necessary and sufficient condition on the local stability of the origin is also provided. Then, based on this discrete equation, a single-species population model is proposed to describe the sterile insect technique for mosquito suppression. Some sufficient conditions on bistability are obtained. There is a stable extinction equilibrium and exactly two periodic orbits. One orbit is a repellor, and the other is an attractor.
