报告题目: The dynamics of a nonlocal dispersal logistic model with seasonal succession

报告时间: 2021年11月25日(星期四), 20:00-21:00

报告地点: 腾讯会议，会议号：180 708 173

内容摘要: This talk includes two parts.

The dyanmics of a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat is considered in the first part, where the time periodicity accounts for the effect of two different seasons. By showing the existence and asymptotic profile of the principal eigenvalue of a time-periodic nonlocal dispersal operator, and applying the time-periodic upper-lower solution method, we obtain the criteria for persistence or extinction of species. Moreover, the limiting profile of positive time-periodic solution is presented here.

The second part of this talk focuses on the free boundary problem of a nonlocal dispersal logistic model with seasonal succession, where the free boundaries $x=g(t),x=h(t)$ represent the expanding front. We prove the existence and uniqueness of global solution, and then examine the long-time dynamical behaviour and the criteria that completely determine when spreading and vanishing can happen, revealing some significant differences from the model without seasonal succession. Moreover, we use a“thin-tail” condition on the kernel function to estimate the asymptotic speeds of $(g,h)$ and the asymptotic spreading speed of $u$, which is achieved by solving the associated semi-wave problem.

报告人简介: 戴斌祥，中南大学数学与统计学院二级教授、博士生导师；湖南省数学学会常务理事、高等教育与大学数学竞赛工作委员会副主任委员；中国生物数学会常务理事；入选湖南省新世纪121人才工程人选；主要从事时滞微分方程与离散动力系统、种群生态学与传染病学、反应扩散方程的定性理论与应用等领域的研究，先后在《Nonlinearity》、《J. Dyn. Diff. Equ.》、《Chaos》、《Appl. Math. Model》等国内外权威期刊上发表学术论文150多篇，主持5项国家自然科学基金面上项目、1项国家973计划子课题、1项湖南省自然科学基金重点项目和多项省部级科研课题，获得湖南省科技进步一等奖和湖南省自然科学一等奖各1项，主编出版教材6部，2020年获得宝钢教育基金优秀教师奖。

欢迎感兴趣的老师和同学参加！