报告题目：Nonlinear Dynamics in Modeling Sea Lice with Stage Structure

报告人：袁沅 教授

报告时间：2025年5月26日19:00-21:00

报告地点：数学与统计学院312

邀请单位：福州大学数学与统计学院，离散数学及其应用省部共建教育部重点实验室，福建省应用数学中心（福州大学）

报告摘要：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.

报告人简介：袁沅，1984年于武汉大学获得学士学位，1988年于中南大学获硕士学位，2002年于加拿大西安大略大学获得博士学位。2002年荣获加拿大国家自然科学基金资助在滑铁卢大学做短暂博士后研究，随后于2002年9月起受聘于加拿大纽芬兰纪念大学。至今，现为该校数学与统计系终身正教授和博士生导师。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 J Appl Math, J Math Biol, JMathAnal Appl, J Differ Eqns, SIAM JAppl Dyn Sys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国家自然科学基金的资助，与中国多所高校同行有科研合作。

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