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宋永利教授学术报告
发布时间:2017-09-21   浏览次数:  

报告题目:Hopf bifurcation in a reaction-diffusion equation with distributed delay and Dirichlet boundary condition(具有分布时滞狄利克雷边界条件的反应扩散方程的Hopf分支)

人:宋永利教授(杭州师范大学

报告时间:20179月22日(周五)下午16:00-16:45

报告地点:理学院一楼报告厅

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 ScienceIEEE Transactions on Neural Networks and Learning SystemsPhysica DNonlinearity 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。