Chapter 5 Functional Differential Equations with State-Dependent Delays: Theory and Applications

This chapter illustrates the recent work on equations with state dependent delays, with emphasis on particular models and on the emerging theory from the dynamical systems point of view. Several new results are presented. The chapter describes examples of differential equations with state dependent delays which arise in physics, automatic control, neural networks, infectious diseases, population growth, and cell production. Some of these models differ considerably from others, and most of them do not look simple. Typically the delay is not given explicitly as a function of what seems to be the natural state variable; the delay may be defined implicitly by a functional, integral or differential equation and should often be considered as part of the state variables.