Dynamics and Numerical Analysis of State Dependent Delay Differential Equations

许多过程都是由具有时滞的微分方程来描述的。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，人类造血系统使白色血细胞更快地成熟。然而，状态依赖性往往是抑制推导数学模型时，这样的过程，因为缺乏的数学理论的状态依赖延迟微分方程。扩展完善的理论和技术，固定延迟的状态依赖领域目前正受到广泛关注，这里详细介绍的研究计划形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.