Stability, bifurcations and response analysis of time delay control system with initial conditions and saturation effects

Applications of bifurcation theory have been employed in all engineering branches, especially in control. In this paper we analyse one control application to delay differential equations based on mentioned bifurcation theory. The time response of a first order delay model with saturation effects has been studied. A stability parameters map, showing the boundaries which separate zones with different qualitative behaviour, has been obtained by analysing the characteristic transcendental equation. Different cases for initial conditions have been employed in our analysis.