報告承辦單位:數學與統計學院
報告題目: 具有抗原性的腫瘤免疫系統的復雜動力學
報告人姓名:Yuming Chen ( 陳玉明）
報告人所在單位:加拿大羅瑞爾大學
報告人職稱: 教授，博士生導師
報告時間:北京時間2021年5月26日（星期三）上午10:00-11:00
騰訊會議號碼:425 930 835
報告人簡介：陳玉明教授分別于1991年和1994年從北京大學獲應用數學學士學位和碩士學位，并于2000年從加拿大約克大學（York University）獲理學博士學位，2000年9月至2001年6月在加拿大阿爾伯塔大學（University of Alberta）做博士后。從2001年7月起，一直任教于加拿大羅瑞爾大學(Wilfrid Laurier University)。現為該校數學系正教授、博士生導師。主要研究興趣為動力系統和泛函微分方程理論及其在生物數學和神經網絡中的應用。美國數學評論及德國數學評論評論員，International Journal of Applied Mathematics and Engineering Sciences, Journal of Applied Mathematics, Mathematics in Applied Sciences and Mathematics等雜志的編委。已在包括 SIAM Journal on Mathematical Analysis, Nonlinearity, Journal of Differential Equations, Physica D, Proceedings of the American Mathematical Society， Mathematical Biosciences, Neural Networks等國際著名刊物發表論文120余篇，其成果被同行廣泛引用，曾獲安大略省科技與創新部早期研究者獎。主持了4項加拿大國家自然科學與工程理事會(NSERC)科研基金項目，參與了3項中國國家自然科學基金面上項目。積極參與高質量人才如碩士生、博士生、博士后的培養。陳教授與中國學者有廣泛交流與合作，曾入選山西省“百人計劃”。
摘要：Taking into account the effect of antigenicity, we propose and analyze a conceptual model for the tumor-immune interaction. The model is described by a system of two ordinary differential equations. Though simple, the model can have complicated dynamical behaviors. Besides the tumor-free equilibrium, there can be at most three tumor-present equilibria. The tumor-present equilibrium can be a saddle or stable node/focus. Sufficient conditions on the nonexistence of nonconstant periodic solutions are provided. Bifurcation analysis including Hopf bifurcation and Bogdanov-Takens bifurcation is carried out. The theoretical results are supported by numerical simulations. Numerical simulations reveal the complexity of the dynamical behaviors of the model, which includes the subcritical/supercritical Hopf bifurcation, homoclinic bifurcation, saddle-node bifurcation at a nonhyperbolic periodic orbit, the appearance of two limit cycles with a singular closed orbit, and so on. Some biological implications of the theoretical results and numerical simulations are also provided.
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