Linear Stability and Bifurcation Analysis
In our study of DDEs, we will mainly concentrate on equations with constant time delay (single or multiple). In particular considering Eq. (1.3), in this chapter we will consider scalar DDEs (n = 1 in Eq. (1.2)) and analyse the linear stability and bifurcation aspects of a class of such equations. We will use the usual method of infinitesimally displacing the solution around the equilibrium point, a geometric approach, and a more general approach to determine linear stability of equilibrium points and then illustrate them with specific examples. We will also point out the extension of these analyses to coupled DDEs/complex scalar equations.