are used widely in real-world models that involve discrete-time lags. Such is the case inpopulation dynamics, where delays arise via maturation times, time-delayed feedback loops in laser devices, and heat transfer lags in atmospheric models. Mathematically, DDEs generate initial value problems in (infinite-dimensional) function spaces and often lead to complicated dynamics. However, the situation simplifies vastly under monotone feedback assumptions.

 

In the talk, I discuss the case when in (1) is

 

The goal will be to show that all the periodic solutions of the DDE (1) arise as solutions to a boundary value problem in two dimensions (rather than infinite).