乐动在线平台(集团)有限公司数学科学学院名师论坛第10期

发布时间:2023-09-24浏览次数:78

报告题目:The integrability and global dynamics of Kolmogorov polynomial differential systems

  人:肖冬梅教授(上海交通大学)

报告时间:2023年9月25日上午10:00-11:00

报告地点数学科学学院A413

内容简介:

In this talk, we first introduce background of planar polynomial differentia systems, then provide a link between the integrability of planar polynomia Kolmogorov differential systems and the intersection number of planar algebraic curves, and obtain algebraic and computational conditions for ruling out the existence of limit cycles. To answer if global dynamics of an integrable system can be completely determined by its local dynamics of all equilibrium points in Poincare disc, we study the Kolmogorov systems with degree n<=3It is proved that the Kolmogorov systems with degree n<=3 are integrable if the number of center-type equilibria or weak saddles of these systems in the interior of quadrants of real plane RA2 reaches the maximum. For these integrable Kolmogorov systems, we give all topological classifications of its global dynamics, which is shown that the local dynamics of the integrable Kolmogorov systems with degree n=2 can completely determine its global dynamics but the local dynamics of the integrable Kolmogorov systems with degree n=3 cannot completely determine its global dynamics. This is based on a joint work with Dr. Hongjin He.

报告人简介:肖冬梅,上海交通大学特聘教授,国家杰出青年科学基金获得者,上海市优秀学科带头人,现兼任中国数学会副理事长、中国数学会数学教育分会副理事长、上海市非线性科学研究会副理事长,教育部数学专业教学指导委员会委员,1991年在北京大学数学系获理学博士学位,1995-1996年在美国加州大学伯克利分校数学系做博十后研究,主要从事微分方程定性理论、分支理论及其应用的研究,与合作者一起在弱化Hilbert第16个问题、高余维分支、非线性系统的全局动力学等方面进行了深入研究,部分成果曾获教育部自然科学一等奖。

(撰稿:梁西银;审核:张国)

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