报告人: 郭上江（湖南大学）
报告题目: Differential equations with state-dependent delay

报告时间：2017年12月22日（星期五）下午4:15-5:15
报告地点：华中科技大学恩明楼813室

报告摘要: In this talk, we consider some kinds of differential equation models with state-dependent delay. One is the existence of a global unstable manifold connecting the positive equilibrium to a slowly oscillating periodic orbit for a Nicholson's blowflies equation with state-dependent delay under a set of mild conditions on the parameters and the delay function. Another is the existence of slowly oscillating periodic solutions of a second-order differential equation with state-dependent delay by using Browder's theorem on the existence of a nonejective fixed point. The last is the global dynamics of 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 and global behaviors of solutions are discussed. These works are jointly completed by Ling Zhang, and Shangzhi Li.