题目：Codimension-two bifurcations in the reaction-diffusion equations and applications to chemical reaction system

时间：2016年4月20日上午10：30                

地点：杭州师范大学下沙校区D楼204学术报告厅

摘要：

In this talk, we consider the codimension-two bifurcation arising from the reaction-diffusion equations. It is a degenerate case and where the characteristic equation has a pair of simple purely maginary roots and a simple zero root. First, the normal form theory for partial differential equations (PDEs) with delays developed by Faria is adopted to this degenerate case so that it can be easily applied to Turing-Hopf bifurcation. Then, we present a rigorous procedure for calculating the normal form associated with the Turing-Hopf and spatial resonance bifurcations of PDEs. We show that the reduced dynamics associated with Turing-Hopf bifurcation is exactly the dynamics of codimension-two ordinary differential equations (ODE), which implies the ODE techniques can be employed to classify the reduced dynamics by the unfolding parameters. Finally, we apply our theoretical results to an autocatalysis model governed by reaction-diffusion equations; for such model, the dynamics in the neighbourhood of this bifurcation point can be divided into six categories, each of which is exactly demonstrated by the numerical simulations; and then according to this dynamical classification, a stable spatially inhomogeneous periodic solution has been found.

专家简介：

宋永利,男,1971年9月生。现为同济大学数学系副教授,博士生导师。2011年入选教育部新世纪优秀人才计划。2005年毕业上海交通大学数学系获理学博士学位。现为国际学术期刊APM和TMA编委。

长期从事时滞微分方程分支理论、混沌控制、神经网络的动力学、时滞耦合系统的稳定性及同步模式、生物系统中的图灵模式等方面的研究工作。已在《Physica D》、 《Journal of Nonlinear Science》、《Nonlinear Analysis》等国际学术期刊上发表学术论文50余篇,被国内外同行他引691次，其中单篇最高引用140次(Physica D,200 (2005)185-204)。2014年,2015年连续两次入选中国高被引学者(Most Cited Chinese Researchers)榜单(数学类)。