演讲人Speaker：    袁沅

题目Title: Stability and Bifurcation in FDE with Distributed Delay

时间Date： 2019  年  12月 3  日       Time：15:00-16:00

地点Venue：A栋  308 室

内容摘要

In some applications of delay differential equations in population dynamics, the need of incorporation of distributed delay is often the result of the existence of some processes or structures. The main objective of the talk is to provide some information of the stability (including local and global stability) and Hopf bifurcation analysis in a general functional differential equation with distributed delay. The local stabilityparameter regions related to time delay are given and compared for a general distribution delay function and three frequently used distributed delays including Dirac, uniform and Gamma distributions. A set of sufficient conditions for the global stability of the positive equilibrium is established for a large class of non-monotone time-delayed differential equations by the method of fluctuations and the exponentialordering approach. With the loss of the stability at the boundary of these regions, we discuss the Hopf bifurcation using normal form method, there the computation of the coefficients are given in the form of the corresponding characteristic equation explicitly. Using the theoretical results we study two examples about white blood cell models and address the effect of the distributed time delay in the physiologicaloscillations. Numerical simulation are illustrated to verify the theoretical predictions.

个人简介(About the speaker):

袁沅，1984年于武汉大学获得学士学位，1988年于中南大学获得硕士学位，2002年于加拿大西安大略大学（University of Western Ontario）获得博士学位。2002年荣获NSERC（加拿大国家自然科学基金）资助在滑铁卢大学(University of Waterloo)做短暂博士后研究，随后于2002年9月起受聘于加拿大纽芬兰纪念大学（Memorial University of Newfoundland）至今，现为该校数学与统计系终身正教授和博士生导师。

袁教授主要研究方向包括非线性动力系统的稳定性及分支分析、时滞微分方程及其在神经网络和生物数学等的应用、微分方程的符号及数值计算方法。现已在SIAM Journal of Applied Mathematics, Journal of Mathematical Biology, Journal of Mathematical Analysis and Applications, Journal of Differential Equations, Nonlinear Analysis: Real World Applications, SIAM Journal on Applied Dynamical Systems等主要应用数学及生物数学杂志发表论文近六十篇。研究成果深受同行好评及引用，研究一直受到加拿大NSERC的资助。