报告题目：Invasion analysis on a predator-prey system in open advective environments

报 告 人：聂 华 教授 陕西师范大学

照    片：

邀 请 人：吴事良 教授

报告时间：2020年10月17日下午4:00-5:00

报告平台：腾讯会议（ID: 589 280 908）

报告人简介：聂华，博士、教授、博士生导师，长期从事生态种群动力学模型的理论研究与数值模拟。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：We investigate a reaction-diffusion-advection system which characterizes the interactions between the predator and prey in advective environments, such as streams or rivers. In contrast with non-advective environments, the dynamics of this system is more complicated. It turns out that there exists a critical mortality rate of the predator and two critical advection rates, which classify the dynamic behavior of this system into two or three scenarios, that is, (i) both populations go extinct; (ii) the predator can not invade and the prey survives in the long run; (iii) the predator can invade successfully when rare and it will coexist permanently with the prey. Specially, the predator can invade successfully when rare if both the mortality rate of the predator and the advection rate are suitably small. Furthermore, by the global bifurcation theory and some auxiliary techniques, the existence and uniqueness of coexistence steady states of this system are established. Finally, by means of numerical simulations, the effects of diffusion on the dynamics of this system are investigated. The numerical results show that the random dispersals of both populations favor the invasion of the predator.