报告题目： On a competition-diffusion-advection system from river ecology: mathematical analysis and numerical study

报 告 人：聂华 教授 陕西师范大学

邀请人：李善兵 副教授

报告时间：2021年10月27日（周三） 15：00-16：00

报告地点：腾讯会议 322 988 250

报告人简介：聂华，教授、博士生导师，研究方向：反应扩散方程与空间生态种群模型。现任中国生物数学学会理事、中国计算数学学会理事。2006年获得博士学位，2012年入选教育部“新世纪优秀人才支持计划”；2015年入选陕西省“青年科技新星”；多次赴美国明尼苏达大学、澳大利亚新英格兰大学、台湾清华大学合作研究与访问。已主持国家自然科学基金项目4项，主持完成省部级项目3项；已在“SIAM J. Appl. Math.”、“SIAM J. Math. Anal.”、“J. Differential Equations”、“J. Math. Biol.”、“Math. Biosci.”、“European J. Appl. Math.”、“Proc. London Math. Soc.”、“Sci. China Math.”等国内外知名刊物上发表学术论文50多篇。

报告摘要： This paper is mainly concerned with a two-species competition model in open advective environments, where individuals cannot pass through the upstream boundary and do not return into the habitat after leaving the downstream end. By the theory of principal eigenvalue, we first obtain two critical curves ($\Gamma_1$ and $\Gamma_2$) in the plane of bifurcation parameters that sharply determine the local stability of the two semi-trivial steady states. Then under various conditions on given parameters, we discuss the global dynamics via different techniques including the comparison principle for eigenvalues and perturbation and compactness arguments, which shows that both competitive exclusion and coexistence are possible. For general values of parameters, we take both analytic and numerical approaches to understand further the potential behaviors of $\Gamma_1$ and $\Gamma_2$, and numerically observe that beside the competitive exclusion and coexistence, the bistable phenomenon is also possible, which is different from the known results of competitive ODE and reaction-diffusion systems (where bistability is impossible). The implication of our numerical results on the future work is also discussed.