Abstract:   Delay differential equation (DDEs) are widely used in many areas, such as mechanical engineering and biological systems. Unlike the systems of ordinary differential equations (ODEs), DDEs have some more complicated properties. For example, the closed form solution even for a linear scalar DDE is usually hard to achieve; the spectrum of DDE is infinite. Most of the interesting results in DDE came out in recent ten years, and a lot of them are based on the theories of Lambert W function. 

In this talk, I will begin with the motivation of study DDEs by giving some simple examples. Then I will talk about the general definition of DDEs by comparing to ODEs. Our focus is introducing basic properties of DDEs, such as numerical solutions, spectrum, stability and bifurcation. After that, I will talk about the Lambert W function and its application. At last, I will show some examples about how we study DDEs using the Lambert W function. 

This talk is very intuitive and only basic ideas about dynamical systems and complex variables are necessary. 

Speaker:  Feng Wei
Institution:  University of Michigan