活动时间：2025-04-10 13:30
活动地点：2号学院楼2432报告厅
主讲人：张祥
主讲人中文简介：
张祥，上海交通大学特聘教授（二级教授、博士生导师），享受国务院特殊津贴。2018年入选欧洲科学与艺术院院士。主要从事常微分方程的定性、分支和可积理论，以及奇异摄动理论及其应用等方面的研究。代表性研究成果发表在《American J. Mathematics》、《Advances in Mathematics》、《Communications in Mathematical Physics》、《Ergodic Theory and Dynamical Systems》、《J. Differential Equations》、《J. Functional Analysis》、《J. Nonlinear Sciences》、《Physical D》、《Pacific J. Mathematics》和《Transaction of American Mathematical Society》等国际重要数学期刊上。现已出版专著《Integrable Theory of Dynamical Systems: Algebra and Analysis》和教材《常微分方程》各一部。近年来多次应邀在德国、法国、西班牙、美国、加拿大、日本和墨西哥等召开的动力系统国际学术会议上做大会特邀报告。现任中国数学会奇异摄动专业委员会主任和上海市数学会理事（曾任中国数学会理事）。担任SCI杂志《Qualitative Theory of Dynamical Systems》和《International Journal of Bifurcation and Chaos》的Associate编辑。
活动内容摘要：
For the Leslie-Gower predator-prey model with Michaelis-Menten type prey harvesting, the known results are on the saddle-node bifurcation and the Hopf bifurcation of codimensions 1, the Bogdanov-Takens bifurcations of codimensions 2 and 3, and on the cyclicity of singular slow-fast cycles. Here we focus on the global dynamics of the model in the slow-fast setting and obtain much richer dynamical phenomena than the existing ones, such as global stability of an equilibrium; an unstable canard cycle exploding to a homoclinic loop; coexistence of a stable canard cycle and an inner unstable homoclinic loop, and consequently coexistence of two canard cycles: a canard explosion via canard cycles without head, canard cycles with short head and beard and relaxation oscillation with short beard. This last one should be a new dynamical phenomenon. Numerical simulations are provided to illustrate these theoretical results.
主持人：吴潇