主講人：牛磊 東華大學(xué)研究員

時(shí)間：2023年5月7日10：30

地點(diǎn)：三號(hào)樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：牛磊，2016-2019年在芬蘭赫爾辛基大學(xué)Mat Gyllenberg教授的團(tuán)隊(duì)做博士后，2020年至今在東華大學(xué)數(shù)學(xué)系工作, 任研究員。主要研究領(lǐng)域包括單調(diào)和競(jìng)爭(zhēng)動(dòng)力系統(tǒng)、應(yīng)用動(dòng)力系統(tǒng)和生物數(shù)學(xué)。代表性成果發(fā)表在JMPA，Nonlinearity，SIADS，JDE，JMB，DCDS-A，Proc. Roy. Soc. Edinburgh A等。2021年入選上海市海外高層次人才計(jì)劃。

內(nèi)容介紹：In this talk, we review the theory of carrying simplex of competitive dynamical systems and some of our 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. We specially establish an index formula on the carrying simplex, by which we obtain which classes have positive fixed points. 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.