报告人: 韩茂安教授、博导(上海师范大学数学系)

报告题目：Expansion of Melnikov Functions and Limit Cycle Bifurcation

时    间：2014年12月19日下午  2:30-3:30

地    点：数计学院4号楼229会议室

报告摘要:  

 The main purpose of this article is to introduce some methods to find the number of zeros of the Melnikov function through studying the expansions of it at a Hamiltonian value corresponding to an elementary center, nilpotent center or a homoclinic or heteroclinic loop with hyperbolic saddles or nilpotent critical points, and then provide some results to produce limit cycles using the first coefficients of the expansions.

专家简介：

上海师范大学教授、博导、国家有突出贡献的中青年专家；曾任上海交通大学数学系常务副主任（主持工作）等，现为上海师范大学数学科学研究所所长、动力系统中心主任、数学博士后流动站负责人等；常微分方程与动力系统领域著名学者，在微分方程定性、分支理论等做出了杰出的工作，曾获教育部科技进步一等奖等，已在JDE、SIAM J. Appl. Math.等杂志发表了系列论文以及Springer等出版社出版了多部专著，其中《Normal forms, Melnikov functions and bifurcation of limit cycles》(与郁培教授合作)被列为Applied Mathematical Sciences第181册，2012年在Springer出版。

韩茂安教授2002年在上海交通大学创办《Communication in Pure and Applied Analysis》杂志并任主编（2002-2005），2011年在上海师范大学创办《Journal of Applied Analysis and Computation》杂志并任主编(该杂志被SCIE收录)；现为《Journal of Applied Analysis and Computation》主编、《Communication in Pure and Applied Analysis》以及《International Journal of Bifurcation and Chaos》等杂志编委。

报告人: Pei Yu(郁培) 教授、博导(加拿大西安大略大学应用数学系)

报告题目：Modelling and Analysis of Recurrent Infections

时    间：2014年12月19日下午3:30-4:30

地    点：数计学院4号楼229会议室

参加对象：微分方程等相关研究方向的老师与研究生

报告摘要:  

 In this talk, we will present dynamic models of recurrent infections in individuals. These viral infections, HIV being a well-known example, have long periods of low viral activity punctuated by episodes of high viral reproduction. Previous models of the dynamics of these viral blips used either stochastic components or forcing terms as the triggers to simulate the phenomenon. The new developed models require neither stochastic features nor forcing terms and generate the viral blips by dynamic bifurcations. Using dynamical systems theory, we hypothesize four conditions for the existence of viral blips in a deterministic in-host infection model. These conditions allow us to develop very simple (2- and 3-dimensional) infection models which produce viral blips, and we determine the complete parameter range for the 3-dimensional model in which blips are possible, using stability analysis. Other possible mechanisms of generating blips will also be discussed.

专家简介：

加拿大西安大略大学应用数学系教授、博导；常微分方程与动力系统领域著名专家，在微分方程定性、分支理论等做出了杰出的工作，已在《SIAM Review》等杂志发表系列论文以及Springer等出版社出版了多部专著，其中《Normal forms, Melnikov functions and bifurcation of limit cycles》（与韩茂安教授合作）被列为Applied Mathematical Sciences第181册，2012年在Springer出版。

郁培教授现任《Journal of Applied Analysis and Computation》、《InternationalJournal of Bifurcation and Chaos》与《Communications in Nonlinear Science and Numerical Simulation》等杂志编委。