報告題目：The integrability and global dynamics of Kolmogorov polynomial differential systems
報 告 人：肖冬梅教授(上海交通大學)
報告時間：2023年9月25日上午10：00-11：00
報告地點：數學科學學院A413
內容簡介：
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.
報告人簡介：肖冬梅，上海交通大學特聘教授，國家杰出青年科學基金獲得者，上海市優秀學科帶頭人，現兼任中國數學會副理事長、中國數學會數學教育分會副理事長、上海市非線性科學研究會副理事長，教育部數學專業教學指導委員會委員，1991年在北京大學數學系獲理學博士學位，1995-1996年在美國加州大學伯克利分校數學系做博十后研究，主要從事微分方程定性理論、分支理論及其應用的研究，與合作者一起在弱化Hilbert第16個問題、高余維分支、非線性系統的全局動力學等方面進行了深入研究，部分成果曾獲教育部自然科學一等獎。
（撰稿：梁西銀；審核：張國）
數學科學學院
2023年9月24日
