Dynamics and Numerical Analysis of State Dependent Delay Differential Equations

许多过程都是用带有时滞的微分方程组来建模的。在大多数模型和数学理论中，这一时滞是固定的，但在应用领域中，有许多证据表明可变时滞取决于系统的状态。例如，当成熟细胞数量较少时，人类造血系统会更快地成熟白细胞。然而，由于状态相关时滞微分方程数学理论的匮乏，在推导这类过程的数学模型时，往往会抑制状态相关性。将固定延迟的成熟理论和技术扩展到依赖状态的领域目前正受到许多关注，这里详细说明的研究计划构成了这一努力的一部分。

Many processes are modelled by differential equations subject to delays. In most models and mathematical theory this time delay is fixed, but in application areas there is much evidence of variable delays which depend on the state of the system. For example, the human hematopoietic system matures white blood cells faster when when mature cell counts are low. However, state dependency is often suppressed when deriving mathematical models of such processes, because of the paucity of the mathematical theory for state-dependent delay differential equations. Extension of the well-established theory and techniques for fixed delays to the state-dependent realm is currently receiving much attention, and the research program detailed here forms a part of this effort.