主讲人简介：袁沅，加拿大纽芬兰纪念大学数学与统计系终身正教授、博士生导师。主要研究方向包括非线性动力系统的稳定性及分支分析、时滞微分方程及其在生物/生态数学、传染病传播与控制、神经网络等的应用、微分方程的符号及数值计算方法。
Functional differential equations provide a powerful framework for modeling complex dynamical processes in mathematical biology,particularly in systems involving time delays,age structure,or stage structure.In this talk,we present several biologically motivated models formulated within this framework,including an age-structured HIV infection model with immune response,a predator–prey system with nonlocal competition and cannibalism,and a stage-structured fish population model with harvesting.We focus on the qualitative analysis of these models,emphasizing the derivation of threshold quantities such as reproduction numbers,and the investigation of local and global stability of equilibria.By employing analytical techniques such as characteristic equations,Lyapunov functionals,persistence theory,and bifurcation analysis,we establish conditions for disease eradication or persistence,population survival,and the impact of key factors such as treatment strategies,intra-species interactions and harvesting policies.These results demonstrate how functional differential equations provide a unified and powerful framework for understanding omplex biological dynamics and offer insights into applications such as disease control and resource management.
