报告人：牛磊，东华大学
报告时间：2023年5月9日（周二）上午 10:00-11:00，腾讯会议， 会议号：219276824.
报告摘要：In this talk, we review the theory of carrying simplex of competitive dynamical systems and some further results for classical competitive mappings. We then discuss a 3D Lotka-Volterra competition model with seasonal succession. We show that the dynamics of the associated Poincaré map can be classified into 33 classes by an equivalence relation relative to the boundary dynamics. In classes 1–18, there is no positive fixed point and every orbit tends to some boundary fixed point. While, for classes 19–33, there exists at least one positive fixed point. We further obtain necessary and sufficient conditions for the uniqueness and nonuniqueness of the positive fixed points when the model has identical intrinsic growth rate and death rate, and then give a complete classification of the global dynamics in this case which has a total of 37 dynamical classes. Especially, we find the interesting phenomena and cases that possess a family of invariant closed curves on which all orbits are positive fixed points, or periodic orbits, or dense orbits.
报告人简介：牛磊， 2016-2019年在芬兰赫尔辛基大学Mat Gyllenberg教授的团队做博士后，2020年至今在东华大学数学系工作, 任研究员。主要研究领域包括单调和竞争动力系统、应用动力系统和生物数学。代表性成果发表在JMPA，Nonlinearity，SIADS，JDE，JMB，DCDS-A，Proc. Roy. Soc. Edinburgh A等。2021年入选上海市海外高层次人才计划。
邀请人：秦文新