Qualitative Analysis and Applications for Dynamical Systems with Time Delay

点击翻译按钮获取中文摘要

Dynamical systems(DSs) with time delay and nonlinearity arise quite naturally in the real world, such as signal propagation, interaction of species, microbiology, epidemiology, physiology, as well as many others, and yet not so much attention has been paid to their analysis, particularly when the delay has certain distribution and the system is symmetric. One of the main purposes in the analysis of DSs in applications is to determine the (long-term) asymptotic behavior of solutions. It is critical to have a full classification of the structure of the qualitative behavior involved in a DS. Although there are some theoretic and applicable results for the DSs with constant delay, there is a lack of theoretical analysis in the systems with distributed time delay. If in addition the system is symmetric, the dynamical properties become much more interesting. Thus, it is necessary to develop and extend the theory and methodology to study delay differential equations(DDEs) deeply and widely. For the applications, this research will focus on the dynamics related to pattern formation in plant morphogenesis and Internet congestion control which are very active and challenging research areas in mathematical biology and engineering.