Dynamics and Numerical Analysis of State Dependent Delay Differential Equations

许多过程是用有时滞的微分方程来模拟的。在大多数模型和数学理论中，这个时间延迟是固定的，但在应用领域中，有很多证据表明，可变延迟取决于系统的状态。例如，当成熟细胞计数低时，人类造血系统的白细胞成熟得更快。然而，由于缺乏状态相关时滞微分方程的数学理论，在推导此类过程的数学模型时，状态相关性往往被抑制。将成熟的固定延迟理论和技术扩展到依赖状态的领域目前受到了很多关注，这里详细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.