Dynamics and Numerical Analysis of State Dependent Delay Differential Equations

状态相关时滞微分方程的动力学和数值分析

• 批准号: 261389-2013
• 负责人: Humphries, Antony
• 金额: $ 1.09万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=525199
• 关键词: Dynamics; Numerical; Analysis; State; Dependent

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.

许多过程都是通过存在延迟的微分方程来建模的。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，有很多证据表明可变延迟取决于系统的状态。例如，当成熟细胞计数较低时，人类造血系统使白细胞成熟得更快。然而，由于状态相关时滞微分方程的数学理论匮乏，在推导此类过程的数学模型时，状态依赖性常常受到抑制。将固定延迟的完善理论和技术扩展到状态相关领域目前受到广泛关注，这里详细介绍的研究计划构成了这项工作的一部分。