报告人：袁沅 加拿大纽芬兰纪念大学
时间：2019年10月14日 4:30-5:30
地点：院楼425
题目：Nonlinear Dynamics in Modeling Sea Lice with Stage Structure
摘要: Sea lice infection is one of the major threats in the marine fishery, especially for farmed salmon. In this work, we propose two mathematical models, one is for the growth of sea lice with a three-stage structure: non-infectious immature, infectious immature and adults where the level of non-infectious immature development depends on the size of the adult population; another is for the control of sea lice with the predator-prey interaction between cleaner fish and sea lice. By using mathematical techniques and an appropriate change of variables, we first describe the nonlinear dynamics by a system of partial differential equations, then transform it into a system of delay differential equations with constant delay. We provide two important indexes: the adult reproduction number Rs for sea lice and the net reproductive number of cleaner fish Rf, address the global dynamics relating to Rs and Rf theoretically, including the global/local stability of the equilibria, uniformly persistence and possible Hopf bifurcation. Numerical simulations are provided to confirm the theoretical results.
袁沅教授简介：2002年毕业于加拿大西安大略大学应用数学专业, 同年入职加拿大纽芬兰纪 念大学, 现为终身教授. 袁教授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神经网络和生物数学等的应用、微分方程的符号及数值计算方法. 现已在SIAM Journal of Applied Mathematics, Journal of Mathematical Biology, Journal of Mathematical Analysis and Applications, Journal of Differential Equations, Nonlinear Analysis: Real World Applications, SIAM Journal on Applied Dynamical Systems等主要应用数学及生物数学杂志发表论文近六十篇. 研究成果深受同行好评及引用, 研究一直 受到加拿大 NSERC的资助.
