Analysis methods for neutral delay differential equations

Abstract

Two different methods for the stability and bifurcation analyses of neutral delay differential equations are presented. The first one relies on classical techniques and it is oriented to the study of the roots of the characteristic equation, which is a transcendental one. It provides a straightforward test to obtain the stability chart in the parameter space of the studied system. The second method uses a frequency-domain approach, based on the control theory, to determine the stability and dynamic bifurcations, and also providing approximations for the smooth oscillations appearing when the system loses its stability.