Time-Delay Systems: An Overview

Abstract

Time-delay naturally arises in many real-world systems, due to the fact that the instantaneous rate of change of such systems does not only depend on their current time but rather on their previous history as well. Hence, time-delays are ubiquitous, their introduction often leads to suppression of oscillations, multistability and chaotic motion in the dynamical systems. This review presents some models with different kinds of time-delays such as discrete, distributed and combination of both discrete and distributed time-delays with special emphasis on the reason of incorporating such delays into the system.