报告题目：Hopf bifurcation in a reaction-diffusion equation with distributed delay and Dirichlet boundary condition（具有分布时滞和狄利克雷边界条件的反应扩散方程的Hopf分支）
报告人：宋永利教授（杭州师范大学）
报告时间：2017年9月22日（周五）下午16:00-16:45
报告地点：bat365在线平台一楼报告厅
报告摘要：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.
报告人简介：宋永利，杭州师范大学教授，2005 年于上海交通大学获博士学位，先后在同济大学和杭州师范大学工作。2011 年起任同济大学博士生指导教师。曾出访西班牙、澳大利亚、加拿大、美国做博士后或合作研究。现为两个国际学术期刊编委。已在Jounal of Differntial Equations, Journal of Nonlinear Science、 IEEE Transactions on Neural Networks and Learning Systems、Physica D、Nonlinearity 等国际学术期刊上发表学术论文60 余篇，其中SCI收录50 余篇。2014 年起连续三年入选中国高被引学者榜单（数学类）。曾主持、或作为项目组主要成员参与完成国家自然科学基金重点项目、面上项目、上海市自然科学项目等十余项。目前正在主持一项国家自然科学基金面上项目的研究工作。2011年入选教育部新世纪优秀人才计划。