报告摘要：Almost all population communities are strongly influenced by their seasonally varying living environments. We investigate the influence of seasons via ordinary differential equations with periodically varying parameters. We consider a seasonally forced predator-prey system with a nonmonotonic functional response in four cases. That is, the system is forced with periodically varying natural death rate, periodically varying carrying capacity, periodically and non-synchronously varying death rate and carrying capacity with the same period, and periodically and non-synchronously varying death rate and carrying capacity with different periods. The four seasonality mechanisms are analysed via numerical bifurcation analysis generating bifurcation diagrams for periodic solutions of period one and two. When the natural death rate is seasonally forced, we get six different bifurcation diagrams corresponding to different bifurcation cases of the unforced system. If the carrying capacity is forced, two different bifurcation diagrams are obtained. Here we can not get a ``universal diagram" like the one in the seasonally forced system with Holling type II functional response; that is, the two elementary seasonality mechanisms have different effects on the system. When both the natural death rate and the carrying capacity are forced with two different seasonality mechanisms, the arising phenomena are to some extent different. The bifurcation results also show that each seasonality mechanism can give rise to multiple attractors including stable cycles of different periods, quasi-periodic solutions, strange attractors, and that catastrophic transitions can occur. In addition, we give some phase portraits and corresponding Poincar\'e map portraits to illustrate different attractors.

报告时间：2017年4月17日（周一）下午4:00-5:00

报告地点：下沙校区教学D楼204室(学术报告厅)

报告人简介：郑州大学数学与统计学院教授，博士生导师，河南省特聘教授。研究方向为常微分方程和应用数学，在J. Nonlinear Sci., Phys. Rev. B, Phys. Rev. E和Sci. Rep.等数学、物理或综合类期刊发表SCI论文53篇。主持完成多项国家自然科学基金项目，河南省杰出青年基金、河南省科技创新杰出人才基金和河南省高校科技创新团队等。获河南省科技进步二等奖（第一完成人）和河南省青年科技奖。教育部新世纪优秀人才，德国洪堡学者，河南省学术带头人。中国工业数学与应用数学学会理事。