CHAPTER 6 - Delay Equations

Abstract

This chapter focuses on the importance of delay equations. Problems in electrodynamics, reactor kinetics, behavior of economic systems, and weapons fire control from moving platforms are all modeled by differential delay equations. The delays may be constant, time dependent, stochastic, or state dependent. The equations may be linear or nonlinear, deterministic, or stochastic. The chapter describes various delay operators for the solution of equations involving retarded effects and deterministic and random delay operators as well. In the simple delay operators, the delays are constants and the delay operator is a deterministic nondifferential operator. Random delay operators are the one that involves random retardation. In the case of time-dependent delays, the delay is time dependent and can be either deterministic or stochastic. The deterministic nonlinear operations Ni(·) and stochastic nonlinear operations i(·) are used to define deterministic and stochastic nonlinear differential delay operations.