報告題目:Codimension-two bifurcations in the reaction-diffusion equations and applications to chemical reaction system

報告地點: 1C324

報告時間：5月4日14：30-16:00

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.

報告人簡介：宋永利,男,1971年9月生。現(xiàn)為同濟大學(xué)數(shù)學(xué)系副教授,博士生導(dǎo)師。2011年入選教育部新世紀(jì)優(yōu)秀人才計劃。2005年畢業(yè)上海交通大學(xué)數(shù)學(xué)系獲理學(xué)博士學(xué)位?，F(xiàn)為國際學(xué)術(shù)期刊APM和TMA編委。長期從事時滯微分方程分支理論、混沌控制、神經(jīng)網(wǎng)絡(luò)的動力學(xué)、時滯耦合系統(tǒng)的穩(wěn)定性及同步模式、生物系統(tǒng)中的圖靈模式等方面的研究工作。已在《Physica D》、 《Journal of Nonlinear Science》、《Nonlinear Analysis》等國際學(xué)術(shù)期刊上發(fā)表學(xué)術(shù)論文50余篇,被國內(nèi)外同行他引691次，其中單篇最高引用140次(Physica D,200 (2005)185-204)。2014年,2015年連續(xù)兩次入選中國高被引學(xué)者(Most Cited Chinese Researchers)榜單(數(shù)學(xué)類)。