Scalar delay differential equations are used to model phenomena in which a previous state of the system plays a role in its future evolution. The explicit inclusion of discrete-time lags produces infinite dimensional dynamical systems whose behavior is often too complex for pure mathematical analysis. However, under a monotone feedback assumption, Mallet-Paret and Sell showed a Poincaré-Bendixson type theorem that turns periodic solutions into cornerstones for the study of global dynamics.

 

In the talk, I will show how, under further symmetry assumptions, periodic solutions of delay differential equations with monotone feedback arise exclusively via a boundary value problem for a two-dimensional ordinary differential equation.