延迟动力系统的延迟依赖散逸性考虑到了延迟量对系统散逸性的影响，有别于现有的散逸性结果。本项目致力于延迟动力系统的解析和数值散逸性分析，寻求新的系统本身延迟依赖散逸性充分条件，并分析线性多步方法，Runge-Kutta方法等重要方法的延迟依赖散逸性。本项目旨在扩充现有的延迟动力系统散逸性研究成果，建立数值格式延迟依赖散逸性准则。所获成果将进一步丰富和发展延迟动力系统的解析和数值散逸性理论。

Delay dependent dissipativity of delay dynamic systems which considers the effect of delay term for the systems are very different from the dissipativity results in the existing literature. This project is concerned with delay-dependent dissipativity analysis of the analytical and numerical solutions for delay dynamical systems. A new sufficient condition of delay dependent dissipativity will be derived. And the numerical delay dependent dissipativity of several classes of methods, including linear multistep methods and Runge-Kutta methods, will be analyzed. This project aims to expand the existing results of dissipativity for delay dynamical systems and establish delay dependent dissipativity criterion of numerical methods. The study will enhance and develop the numerical and analytical dissipativity theory for delay dynamical systems.