The mathematics of delay equations with an application to the Lang-Kobayashi equations

For dynamical systems governed by feedback laws, time delays arise naturally in the feedback loop to represent effects due to communication, transmission, transportation or iternia effects. The introduction of time delays in a system of differential equations results in an infinite dimensional state space. We give an introduction to the basic theory of delay equations. After this introduction we illustrate the theory with a local analysis of the Lang-Kobayashi equations describing a laser with delayed optical feedback.