Introduction

Differential equations are a basic yet powerful mathematical apparatus for studying real world objects and phenomena. These equations, when used as models and combined with information technology tools, allow us to conduct theoretical investigations and to predict the behavior of real systems. However, since real life processes are quite intricate, complex mathematical equations are required to study them. One natural setting is the case of evolutionary equations using past history. These equations are now referred to as functional differential equations. Picard (1908), at the international congress of mathematicians, stressed the importance of functional differential equations in physical problems. Interest in this topic increased after 1940, but there was little progress on qualitative theory until the mid-1950s. Perhaps the reason was that even though the evolution of the system at present time was determined by some of the past history, the primary object of study was where the system was at the present time. In 1956 Krasovskii made the important observation that the state of a system at any time described by a functional differential equations should be the system at that time together with the past history that is required to determine the future evolution of the system. With his contribution, he made a huge impact on the qualitative investigations of functional differential equations. By the early 1970s, a framework for the qualitative theory of functional differential equations had been outlined. In the last decades, different qualitative properties of the solutions of functional differential equations have been obtained (see, for example, monographs [El’sgol’ts and Norkin 1973], [Hale 1977], [Hale and Lune 1993], [Kolmanovski and Nosov 1986] and references cited therein).