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: 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=524747
• 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.

时滞微分方程在数学生态学、种群生物学和神经网络等领域有着广泛的应用。众所周知，在生物网络和人工神经网络中，由于信息的处理而产生延迟。时滞微分方程是无穷维动力系统，由于时滞引起的动力学性质更丰富，因此比常微分方程更具有挑战性和研究价值。该项目的目的是为延迟微分方程的局部和全局动力学，特别是其全局吸引子的理解做出重大贡献。