報告題目：Hopf bifurcation in a reaction-diffusion equation with distributed delay and Dirichlet boundary condition（具有分布時滯和狄利克雷邊界條件的反應擴散方程的Hopf分支）
報告人：宋永利教授（杭州師範大學）
報告時間：2017年9月22日（周五）下午16:00-16:45
報告地點：必一体育平台一樓報告廳
報告摘要：The stability and Hopf bifurcation of positive steady state solutions to a general scalar reaction-diffusion equation with distributed delay and Dirichlet boundary condition are investigated in this paper. The time delay follows a Gamma distribution function. Through analyzing the corresponding eigenvalue problems, we rigorously show the occurrence of Hopf bifurcations when the shape parameter $n$ is greater than $1$, and the steady state is always stable when $n=0$. By computing normal form on the center manifold, the direction of Hopf bifurcation and the stability of the periodic orbits are also be determined under a general setting. Our results show that the number of Hopf bifurcation delay values is finite and increasing in $n$, which is significantly different from the discrete delay case, and the first Hopf bifurcation value is also decreasing in $n$. Examples from population biology and numerical simulations are used to illustrate the general results. This is a joint work with Q. Shi and J. Shi.
報告人簡介：宋永利，杭州師範大學教授，2005 年於上海交通大學獲博士學位，先後在同濟大學和杭州師範大學工作。2011 年起任同濟大學博士生指導教師。曾出訪西班牙、澳大利亞、加拿大、美國做博士後或合作研究。現為兩個國際學術期刊編委。已在Jounal of Differntial Equations, Journal of Nonlinear Science、 IEEE Transactions on Neural Networks and Learning Systems、Physica D、Nonlinearity 等國際學術期刊上發表學術論文60 余篇，其中SCI收錄50 余篇。2014 年起連續三年入選中國高被引學者榜單（數學類）。曾主持、或作為項目組主要成員參與完成國家自然科學基金重點項目、面上項目、上海市自然科學項目等十余項。目前正在主持一項國家自然科學基金面上項目的研究工作。2011年入選教育部新世紀優秀人才計劃。