Dynamics of delay differential equations: theory and applications

时滞微分方程动力学：理论与应用

• 批准号: 249679-2009
• 负责人: Chen, Yuming
• 金额: $ 1.02万
• 依托单位: Wilfrid Laurier University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503724
• 关键词: Dynamics; delay; differential; equations; theory

Delay differential equations have arisen naturally in many applications such as mathematical ecology, population biology, and neural networks. It is well known that, both in biological and artificial neural networks, delay arises because of the processing of information. Delay differential equations are infinite dimensional dynamical systems and hence are more challenging and interesting to study than ordinary differential equations as delays induce richer dynamics. The purpose of this project is to make significant contributions to the understanding of the local and global dynamics of delay differential equations, especially their global attractors.

在数学生态学，人群生物学和神经网络等许多应用中，自然而然地出现了延迟微分方程。众所周知，在生物学和人工神经网络中，由于信息的处理而出现延迟。延迟微分方程是无限尺寸动力学系统，因此比普通微分方程更具挑战性和有趣的研究，因为延迟引起了更丰富的动力学。该项目的目的是为理解延迟微分方程的本地和全球动态做出重大贡献，尤其是其全球吸引子。