一、题目: Differential equations with state-dependent delay
二、主讲人：郭上江教授
三、时 间：2016年11月25日，下午：15:00-15: 45（周五）
四、地 点：闻理园A4-305室
报告摘要: In this talk, we first consider some kind of differential equation models with state-dependent delay. One is the existence of slowly oscillating periodic solutions for a Nicholson's blowflies equation with state-dependent delay under a set of mild conditions on the parameters and the delay function. In particular, when the positive equilibrium gets unstable, a global unstable manifold connects the positive equilibrium to a slowly oscillating periodic orbit. Another is a cooperative model composed of two species with stage structure and state-dependent maturation delays. It is shown that the solutions of the two mature equations are always positive and that all the solutions of the model are bounded above only if the coupling strength is small enough. If the coupling strength is large enough then the solutions of the model tends to infinity as the time tends to infinity. The positivity of the solution of the two immature populations has been established under some additional conditions. The existence and patterns of equilibria are investigated by means of degree theory and Lyapunov-Schmidt reduction. The stability of the equilibria is also discussed. Finally, global behaviors of solutions are discussed. The last is a classical van der Pol equation with state-dependent delayed feedback. Firstly, solutions near equilibria are constructed using perturbation methods to determine the sub/supercriticality of the bifurcation and hence their stability. Then, we choose a few examples of state-dependant delay to test our analytical results by comparing them to numerical continuation.
报告人简介：郭上江，湖南大学数学与计量经济学院教授、博士生导师。2004年获得博士学位，2008年被聘为教授。主要从事泛函微分方程的分岔理论研究。先后在英国帝国理工学院和巴斯大学、美国佐治亚理工学院数学系（高级访问学者），加拿大Wilfrid Laurier大学和York大学、匈牙利Szeged大学Bolyai研究所等等国外知名高校访问。在 Journal of Differential Equations , Zeitschrift Fur Angewandte Mathematik Und Physik, Proceedingsof the American Mathematical Society和Nonlinearity 等国际高水平杂志上发表论文近30篇，在Springer出版了一部时滞动力系统分岔理论专著。主持国家自然科学基金面上项目3项，国家自然科学基金青年项目1项。2007年入选教育部新世纪优秀人才支持计划人选。
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2016年11月21日
