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。現為同濟大學數學系副教授,博士生導師。2011年入選教育部新世紀優秀人才計劃。2005年畢業上海交通大學數學系獲理學博士學位。現為國際學術期刊APM和TMA編委。長期從事時滯微分方程分支理論、混沌控制、神經網絡的動力學、時滯耦合系統的穩定性及同步模式、生物系統中的圖靈模式等方面的研究工作。已在《Physica D》、 《Journal of Nonlinear Science》、《Nonlinear Analysis》等國際學術期刊上發表學術論文50余篇,被國內外同行他引691次，其中單篇最高引用140次(Physica D,200 (2005)185-204)。2014年,2015年連續兩次入選中國高被引學者(Most Cited Chinese Researchers)榜單(數學類)。