Modeling with Delay Differential Equations

Abstract

Although modeling phenomena with differential equations has a long and successful history over a wide range of applications, some situations lend themselves to adaptations that more seamlessly capture the entity being modeled. This chapter studies one such adaptation called a delay differential equation (DDE). A DDE is an ordinary differential equation that permits dependencies on historical information, and initial conditions are replaced with legacy assumptions that detail the solution’s previously observed behavior. A DDE is a welcome framework for processes that naturally depend on historical trajectories and not just initial values.