报告题目：On the study of limit cycles for a class of population models with time-varying factors

报告人：黄健沨教授，暨南大学

报告时间：2025年4月3日（周四）10:30-11:30

报告地点：20-306

报告摘要：In this talk, we introduce the study for a class of population models with time-varying factors, represented by one-dimensional piecewise smooth autonomous differential equations. We provide several derivative formulas in ``discrete'' form for the Poincar\'{e} map of such equations, and establish a criterion for the existence of limit cycles. These two tools, together with the known ones, are then combined in a preliminary procedure that can provide a simple and unified way to analyze the equations. As an application, we prove that a general model of single species with seasonal constant-yield harvesting can only possess at most two limit cycles, which improves the work of Xiao in 2016. We also apply our results to a general model described by the Abel equations with periodic step function coefficients, showing that its maximum number of limit cycles, is three. Finally, a population suppression model for mosquitos considered by Yu \& Li in 2020 and Zheng et al. in 2021 is studied using our approach.

报告人简介：黄健沨，中山大学理学博士，复旦大学博士后，现任职于暨南大学信息科学技术学院数学系，教授，博士生导师。研究方向为微分方程定性理论，目前主要关注微分系统的极限环及其衍生问题。在JDE、SIADS、DCDS-A等本领域的国际主流期刊发表论文20余篇。主持国家自然科学基金、广东省自然科学基金、中国博士后科学基金面向项目等项目。获2019广东省自然科学技术奖二等奖（排名第三）。

邀请人：戴燕飞