报 告 人：阮士贵，美国迈阿密大学

报告题目：Homoclinic Bifurcations with Applications to Biological Systems

报告摘要：For n-dimensional differential equations, a homoclinic orbit associated to a hyperbolic equilibrium point is an orbit that has the point as its α-limit set as well as its ω-limit set. Since a homoclinic orbit is structurally unstable, bifurcation occurs when the homoclinic loop is broken. There are two approaches to study such bifurcations: Melnikov function and Shilnikov approach. In this talk, we introduce Shilnikov method in studying homoclinic bifurcations. For planar systems, a homoclinic orbit associated to a saddle will induce a limit cycle under certain condition. For 3-dimensional systems, there are two types of hyperbolic equilibrium points: saddle and saddle-focus. Under various conditions, a homoclinic orbit associated to a saddle will bifurcate to a (stable or saddle) cycle, whereas a homoclinic orbit associated to a saddle-focus will bifurcate to either a stable cycle or infinitely many saddle cycles (that is, chaos) via Smale horseshoe map. Applications to homoclinic bifurcations and chaos in various biological models, including FitzHugh–Nagumo neuron model, three-species food chain models, green ocean plankton models, epileptic models, and chemostat models, will be presented. Generalizations to infinite dimensional systems will be briefly discussed.

报告时间：2021年10月10日（周日）上午9:00

报告地点：腾讯会议（ID：338 625 371）

报告人简介：阮士贵，1983年本科毕业于华中师范大学数学系，1988年获得华中师范大学数学系硕士学位，1992年获得加拿大阿尔伯特(Alberta)大学数学系博士学位，1992-1994年在加拿大菲尔兹数学所(Fields Institute)和麦克马斯特(McMaster)大学做博士后。1994-2002年在加拿大道尔豪斯(Dalhousie)大学数学与统计系先后任助理教授和副教授。现为美国迈阿密大学(University of Miami)数学系终身教授。主要研究领域是动力系统和微分方程及其在生物和医学中的应用，在包括《PNAS》、《Math Ann》、《Memoirs Amer Math Soc》、《Lancet Infect Dis》、《J Math Pures Appl》等学术期刊上发表了约200篇学术论文，受到了国内外同行的关注与大量引用，2014 和2015年连续被汤森路透集团列为全球高被引科学家。担任了一些重要学术期刊如《BMC Infectious Diseases》、《Bulletin of Mathematical Biology》、《DCDS-B》、《Mathematical Biosciences》等的编委，是《Mathematical Biosciences and Engineering》的主编（数学）。作为项目负责人多次获得美国国家卫生研究院（NIH）、美国国家科学基金（NSF）、国家自然科学基金、海外及港澳学者合作研究基金资助。