在工程及自然系统中，存在大量的相对短暂的扰动使系统状态发生改变，这种状态的突然变化使得系统不能单纯地用连续动力系统或者离散动力系统来描述，而要借助于状态脉冲动力系统或(脉冲)状态反馈控制系统，我们称之为“半连续动力系统”(简称SCDS)，这类系统较之单纯的离散或者连续系统，具有极其复杂的动力学行为。本项目在前期工作的基础上，针对SCDS理论及应用领域中的一些关键及困难问题开展研究，主要包括：(1)各类周期解轨道稳定性判定方法的建立，研究SCDS参数变化时，其周期解随参数变化而变动的规律; (2)用压缩映像原理代替后继函数方法, 研究高维SCDS，通过三维SCDS的极限系统来研究三维系统解的性态; (3)以最优化控制和SCDS理论方法为基础，研究害虫综合防治以及野蚊子控制策略的生物经济学问题，以及相应参数对控制效果的影响，为一些实际问题的控制策略提供数学理论依据。

In engineering and natural systems, there are a lot of relatively short perturbations which can change the system states. Such systems cannot be well described by continuous or discrete dynamical systems alone due to these sudden changes, but we can do it by means of state impulsive dynamical systems or (impulsive) state feedback control systems which are called by Semicontinuous Dynamical System (SCDS). Compared with continuous or discrete dynamical systems, this kind of systems have many extremely complicated dynamic behaviors. Based on the previous work, this project will study the key issues and difficult problems in the theory and applications of SCDS which mainly include : (1) establish criteria for orbital stability of all kinds of periodic solutions and examine how periodic solutions would be affected by parameters change of SCDS; (2) explore high-dimensional SCDS by contraction mapping principle instead of successor function method and analyze solution behavior of three-dimensional SCDS by use of limit systems of the SCDS ; (3) based on optimal control and SCDS theoretical method, our research would be focused on biological economical problems such as Integrated Pest Management and wild mosquito control strategies, and revealing the impact of relevant critical parameters on control effect with a view to providing mathematical theoretical foundation for the control strategies of some practical problems.